Design and Experimental Validation of a Passive Following System for a Mecanum-Wheel Mobile Platform Based on Gimbal Posture Perception and Orthogonal Odometry Fusion

Featured Application

The proposed gimbal-guided passive following system can be applied to low-perception-dependence indoor companion and transport platforms, such as medical and rehabilitation carts, warehouse and laboratory material-handling robots, hotel or exhibition service robots, and tethered air–ground cooperative systems. By combining direct physical intention sensing with orthogonal odometry feedback, the system provides an intuitive and robust following solution for Mecanum-wheel mobile bases operating in confined and dynamic environments where vision- or LiDAR-dependent following may be unreliable or unnecessarily complex.

Abstract

Indoor companion, rehabilitation, logistics, laboratory transport, and service robot scenarios require mobile platforms that can follow a human operator safely and flexibly under lighting changes, occlusion, texture-poor corridors, and dynamic pedestrian environments. Vision-, LiDAR-, and UWB-based following systems can provide high perception capability, but their deployment cost, environmental dependence, and sensing complexity remain limiting factors for low-perception-dependence applications. This paper presents a passive following system for a Mecanum-wheel mobile platform based on gimbal posture perception and orthogonal odometry fusion. A rope-tensioned two-axis gimbal is mounted above a 300 mm × 300 mm × 150 mm omnidirectional chassis, and a six-axis inertial sensor installed at the top of the gimbal detects pitch and roll changes induced by user traction. A piecewise posture-to-velocity mapping model with a dead zone, saturation, low-pass filtering, and acceleration limiting converts the user’s traction intention into planar velocity commands in the vehicle coordinate frame. To reduce pose errors caused by Mecanum-wheel slip and discontinuous roller-ground contact, two orthogonal passive odometry wheels and inertial attitude estimation are fused to provide planar position feedback for closed-loop following. A prototype was implemented using an Infineon TRAVEO CYT4BB77 controller, TI DRV8701E motor drivers, six-axis IMUs, magnetic encoders, and an embedded display interface. Experiments evaluated attitude estimation accuracy, planar localization accuracy, passive following performance, gyroscope compensation, and open-loop/closed-loop following. The compensated attitude module achieved a static yaw drift of 0.45 deg/h and a dynamic attitude RMSE below 0.56 deg. Orthogonal odometry fusion produced an average positioning error of 3.8 mm over a 3000 mm linear displacement, reducing error by approximately 84.6% compared with pure Mecanum-wheel drive odometry. In a 5000 mm forward traction task, closed-loop following reduced the average distance error from 38.6 mm to 11.5 mm compared with open-loop attitude mapping. The results indicate that the proposed gimbal-orthogonal odometry architecture provides a compact, intuitive, and environment-robust solution for passive following on omnidirectional mobile platforms.

1. Introduction

Omnidirectional mobile platforms are increasingly used in indoor service, logistics, rehabilitation, and human-assistance applications because they can translate laterally, move diagonally, and rotate in place within confined spaces. Among common wheeled mobile robot architectures, the four-Mecanum-wheel chassis is attractive because it provides holonomic planar motion with relatively simple mechanical construction and compact footprint [1]. This capability is useful for companion transport in hospitals and rehabilitation centers, shelf-to-shelf handling in warehouses and laboratories, and service robots operating in exhibition halls, airports, and hotels. Recent work on assistive mobility also shows that Mecanum and omni-wheel technologies are promising for maneuvering in constrained environments, although stability, control complexity, uneven-ground robustness, and cost remain major challenges [2]. Clinical and rehabilitation-oriented systems using Mecanum wheels further illustrate the potential of omnidirectional platforms for over-ground walking assistance [3].

For mobile robots that operate near humans, following control can be realized through multiple sensing and interaction modalities. High-level perception methods, such as visual tracking, LiDAR-based target detection, SLAM, and UWB localization, can estimate human–robot relative pose without physical contact. However, they require sufficiently observable environments, reliable target association, and sometimes expensive or infrastructure-dependent sensors. Camera-based systems are sensitive to lighting variation, occlusion, and clutter; LiDAR and SLAM systems can fail in geometrically repetitive or texture-poor indoor corridors; and UWB systems require anchors or tags that may not be convenient in temporary deployments. These limitations are not fatal for autonomous navigation, but they become important when the engineering objective is a low-cost, low-perception-dependence companion platform that can be deployed quickly and guided naturally by a nearby user.

Physical human–robot interaction (pHRI) provides an alternative route. Instead of inferring human intent from remote perception, the robot can sense physical input applied by the user and transform it into motion commands. Force-guided mobile platforms and compliant-arm systems have shown that direct physical guidance can be an intuitive way to command robot motion [4]. More general pHRI control research also emphasizes the importance of mapping measured forces or motions to stable robot motion through impedance or admittance principles [5]. For a companion cart or indoor handling platform, a user often does not need a fully autonomous follower; the practical requirement is that the platform should move in the intended direction with low cognitive load, moderate compliance, and predictable behavior. A rope-tensioned interaction structure can satisfy this requirement while avoiding the need for high-level external perception.

Mecanum-wheel platforms also present a specific localization problem. Although the drive wheels are equipped with encoders, the relationship between wheel rotation and platform displacement is affected by roller contact state, load distribution, acceleration, floor friction, and instantaneous slip. Pose estimation based only on drive-wheel odometry can therefore accumulate errors during acceleration, emergency stops, lateral motion, and diagonal motion. Recent studies on Mecanum platforms have addressed pose estimation and control using EKF-based sensor fusion [6], unknown input and uncertainty estimation [7], disturbance-observer-enhanced control [8], command-to-motion modeling [9], and intelligent path planning or fuzzy control [10]. These methods improve different layers of the Mecanum platform performance, but a mechanically independent displacement measurement source remains valuable when drive-wheel slip contaminates odometry.

Orthogonal passive-wheel odometry provides such an independent measurement source. Orthogonal odometers use passive wheels arranged along perpendicular axes to directly measure planar displacement with encoders. Because these wheels are not used for propulsion, their encoder readings are less coupled to drive torque, roller slip, and motor transients. Previous work on orthogonal wheel odometers demonstrated that such systems can achieve centimeter-level positioning in relative coordinate frames and can reduce the effect of wheel slip and ground irregularity by using driven or passive sensing structures [11]. Related Chinese theses and engineering studies on inertial-sensor and orthogonal odometry planar localization further show the feasibility of combining MEMS attitude estimation, encoder odometry, coordinate transformation, and software compensation for indoor robot positioning [12,13]. Multi-sensor fusion and robust control studies also support the idea that improved localization quality directly benefits following and formation control performance [14].

To make the positioning of the work clearer, the related systems can be viewed along two complementary axes: the interaction interface used to infer the operator’s intention and the localization method used to estimate the motion of the mobile base. Vision-, LiDAR-, and UWB-based following methods emphasize remote perception but depend on environmental observability or external infrastructure. Force-guided handles and admittance-controlled platforms provide direct physical interaction, but they usually require calibrated force sensing or compliant arms. Conventional Mecanum platforms provide omnidirectional mobility, but their drive-wheel odometry is sensitive to roller-ground contact and slip. The present study addresses the intersection of these issues by combining a rope-tensioned gimbal posture interface with an independent orthogonal passive-wheel odometry module.

Accordingly, the novelty of the proposed system lies not in the Mecanum-wheel chassis alone, but in the complete low-perception-dependence following chain: physical traction intention is converted into pitch and roll posture, the posture signal is mapped into bounded planar velocity commands, and the realized motion is corrected using odometry that is mechanically decoupled from the drive wheels. This design reduces dependence on ambient perception and mitigates the localization error that would otherwise arise from Mecanum-wheel slip.

This paper builds on these ideas but addresses a different problem: passive following of a Mecanum-wheel platform through a low-perception-dependence physical interaction interface. The proposed system combines a rope-tensioned gimbal for intention perception with orthogonal passive-wheel odometry for planar pose feedback. The gimbal translates the user’s pulling direction and intensity into pitch and roll changes, while the orthogonal odometry module provides real-time planar displacement feedback independent of the Mecanum drive wheels. MEMS attitude estimation, gyroscope drift compensation, and filtering are used to stabilize the posture signal, drawing on established inertial measurement and signal processing techniques [15,16,17].

Broader person-following studies further clarify the research gap addressed here. Comprehensive reviews classify person-following robots by perception modality, interaction mode, and autonomy level [18]. Camera- and laser-based systems demonstrate the remote-perception route [19,20], whereas deep visual tracking, UWB following, and robust image-based tracking remain dependent on reliable sensing, target association, or infrastructure [21,22,23]. Reviews of autonomous mobile robots and sensor fusion challenges identify localization robustness as a persistent limitation [24], and Mecanum-specific drift compensation studies show that omnidirectional bases require explicit treatment of slip, sensor bias, and drift [25]. These studies indicate that a low-perception-dependence physical interface combined with mechanically independent odometry can reduce limitations of perception dependence and drive-wheel slip.

The main contributions of this paper are as follows:

• A passive following interaction method is proposed based on rope-tensioned gimbal posture perception. The method uses pitch and roll angle changes in a gimbal-mounted six-axis IMU to infer the user’s traction intention without relying on vision, LiDAR, or other high-level environmental perception.
• A posture-to-velocity mapping model is constructed for natural interaction control. The model maps gimbal pitch and roll angles to forward-backward and lateral velocity commands, respectively, and incorporates dead-zone suppression, velocity saturation, low-pass filtering, and acceleration limiting.
• Orthogonal passive-wheel odometry is fused with inertial attitude estimation to construct a planar localization feedback loop for the Mecanum-wheel platform. The scheme reduces the influence of drive-wheel slip and discontinuous Mecanum roller-ground contact on pose estimation.
• A prototype system is implemented and experimentally evaluated. Attitude estimation, localization accuracy, passive following, gyroscope compensation, orthogonal odometry, and closed-loop feedback are quantitatively compared.

The remainder of this paper is organized as follows. Section 2 describes the system architecture, mechanical design, hardware implementation, coordinate systems, posture-to-velocity mapping, attitude estimation, orthogonal odometry, and experimental protocol. Section 3 reports the experimental results. Section 4 discusses the significance, engineering applicability, and limitations of the system. Section 5 concludes the paper and presents future work.

2. Materials and Methods

2.1. Overall System Architecture

As shown in Figure 1, the proposed passive following system is organized as a four-layer architecture: mechanical platform, perception, computation, and control. The mechanical platform layer consists of a four-Mecanum-wheel chassis, a rope-tensioned two-axis gimbal, and an orthogonal passive-wheel odometry module. The perception layer includes the gimbal-mounted six-axis IMU, a chassis attitude sensor, magnetic encoders on the orthogonal passive wheels, and an embedded display interface. The computation layer performs inertial data preprocessing, attitude estimation, gyroscope error compensation, posture-to-velocity mapping, orthogonal odometry calculation, coordinate transformation, and feedback correction. The control layer generates motor commands for omnidirectional motion and updates the display interface.

During operation, the user pulls the rope attached to the gimbal. The gimbal deflects about its pitch and roll axes, while yaw is constrained by the mechanical structure. The top-mounted IMU measures the resulting posture changes. The system maps the measured pitch and roll angles to target velocities in the vehicle coordinate frame. At the same time, orthogonal passive wheels measure platform displacement increments, and inertial attitude estimation provides heading information. The platform’s planar pose in the navigation coordinate frame is recursively estimated and used to correct the following motion. The complete control chain is therefore:

Figure 2 organizes the system into seven numbered modules. Modules 1–5 show the main operation sequence. User traction acts on the rope and gimbal, and the six-axis IMU measures pitch and roll posture. The posture-to-velocity mapping module then applies dead-zone processing, piecewise mapping, low-pass filtering, and acceleration limiting. The Mecanum kinematics module converts the vehicle-frame command Vx, Vy, and omega_z into target wheel speeds for platform motion.

Module 6 shows the closed-loop feedback path. Orthogonal passive-wheel odometry supplies encoder-based displacement increments, inertial attitude estimation supplies the heading angle psi, and sensor fusion estimates x, y, and psi. The resulting pose feedback is returned to the motion-control module as a position-error correction signal.

The power-supply architecture is shown as Module 7. A 6S LiPo battery (22.2 V nominal, 25.2 V fully charged) directly supplies the chassis motors and motor drivers through the high-voltage power path. A DC-DC buck converter steps 22.2 V down to a regulated 3.3 V for low-power sensors, including the orthogonal passive-wheel odometry encoders, IMU/gyroscope, magnetometer, and gimbal sensors. Solid red arrows denote the high-voltage path, whereas dashed red arrows denote the regulated 3.3 V path.

2.2. Mechanical Design

2.2.1. Mecanum-Wheel Chassis

The prototype uses a compact four-wheel independent-drive Mecanum chassis with approximate dimensions of 300 mm × 300 mm × 150 mm. Four Mecanum wheels are symmetrically arranged in a rectangular layout. By controlling the speed and direction of the four wheels, the platform can perform forward-backward translation, lateral translation, diagonal motion, and in-place rotation. This motion capability is well-suited to narrow indoor environments, where the platform may need to follow a user through corridors, around shelves, or beside beds and instruments.

The rectangular 300 mm × 300 mm layout was selected to keep the prototype compact while preserving symmetric wheel spacing for forward-backward, lateral, diagonal, and in-place rotational motion. This geometry is functional for indoor operation because the platform can translate laterally in narrow passages without first rotating its body. Compared with general all-directional platforms such as modular Mecanum research bases, the present platform is optimized for rope-guided passive following rather than autonomous navigation or payload-agnostic service operation. The rectangular form is therefore suitable for the current proof-of-concept, although rounded or protected outer packaging would be preferable for crowded clinical, hotel, or exhibition environments.

The same mechanical feature that enables omnidirectional motion also affects odometry reliability. Mecanum wheels generate lateral components through passive rollers. Their contact state depends on load distribution, roller position, floor material, and acceleration profile. During rapid starts, stops, or diagonal motion, wheel-ground slip and roller contact discontinuity can cause drive-wheel encoder odometry to deviate from actual chassis displacement. This motivates the addition of orthogonal passive-wheel odometry as an independent planar displacement source.

2.2.2. Gimbal-Rope Interaction Mechanism

The gimbal-rope interaction mechanism is the main human–robot interface of the system. A two-axis orthogonal gimbal is mounted above the chassis. A rope is connected to the upper end of the gimbal, and a six-axis IMU is rigidly fixed near the top of the gimbal. When a user pulls the rope, the gimbal rotates about pitch and roll axes. The pitch angle represents the forward-backward component of the traction intention, while the roll angle represents the lateral component. The yaw angle is mechanically constrained and is not used as the primary intention signal.

The gimbal is used as a lead-input device rather than as a sensor for autonomous target tracking. A forward or backward traction component mainly changes the pitch angle, whereas a lateral traction component mainly changes the roll angle. When the pulling direction is oblique, both axes are excited, and the controller generates combined longitudinal and lateral velocity commands. The control axes are equipped with the gimbal-mounted six-axis IMU; the orthogonal odometry axes are equipped with magnetic encoders on the passive wheels.

The prototype does not impose a single fixed rope-tension threshold for operation. Instead, the motion command is triggered by posture deflection after the dead-zone threshold is exceeded. The force required to produce this deflection depends on rope length, rope attachment height, gimbal stiffness, user height, and pulling posture. Therefore, we clarify that the present implementation is posture-threshold operated rather than force-threshold operated, and future work should identify adaptive calibration parameters for different users and rope configurations.

As shown in Figure 3, the left model represents the neutral configuration without traction, whereas the right model illustrates the deflected configuration when the user pulls the rope. The deflection is measured as pitch and roll changes and is used as the input for platform motion control.

Compared with button-based or joystick-based operation, the gimbal-rope interface preserves the physical intuition of pulling a cart. Compared with force sensors installed in handles, the proposed structure uses posture perception rather than direct force measurement, reducing sensing complexity. The interaction signal is also independent of ambient lighting and environmental geometry, which is useful in low-perception-dependence applications.

In Figure 3, the upper ring provides the rope attachment point, the middle joint allows two-axis angular deflection, and the lower mounting flange fixes the mechanism to the mobile platform. The IMU is mounted close to the top structure so that the measured pitch and roll angles represent the user-applied traction direction.

2.2.3. Orthogonal Passive-Wheel Odometry Module

The orthogonal odometry module uses two passive omnidirectional wheels installed under the chassis. Their measurement axes are aligned with the vehicle coordinate axes. Each passive wheel is coupled with a magnetic encoder to measure wheel rotation. Because the wheels are passive and are not driven by motors, their measurements are less affected by the drive torque and slip of the Mecanum wheels.

The geometry of this wheel section is functional. The two non-driven passive omnidirectional wheels are used only for displacement sensing, not for propulsion. Each passive wheel has a diameter of 65 mm (radius of 32.5 mm), and the two sensing axes are theoretically arranged at an included angle of 90 degrees. This orthogonal arrangement separates longitudinal and lateral displacement increments in the vehicle frame. It also reduces the influence of the Mecanum drive torque, roller contact discontinuity, and wheel slip on the odometry measurement.

Let the two passive-wheel radii be $R_0$ and $R_1$, and let the encoder pulse increments during one sampling interval be $∆en{c}_0$ and $∆en{c}_1$. If the encoder resolution is $N$ pulses per revolution, the displacement increments measured by the two passive wheels are:

Here, R₀ and R₁ denote the radii of the two passive odometry wheels, Δenc0 and Δenc1 are the encoder count increments over one sampling interval, N is the encoder resolution in pulses per revolution, and Δs₀ and Δs₁ are the corresponding wheel displacement increments. The vector $∆p_b={\left[∆x_b,∆y_b\right]}^T$ represents the planar displacement increment in the vehicle frame. The calibration matrix Cα compensates for the measured non-orthogonality angle α between the two passive-wheel measurement axes.

$$∆s_0={\displaystyle \frac{2\pi R_0}{N}}∆en{c}_0,$$

(1)

$$∆s_1={\displaystyle \frac{2\pi R_1}{N}}∆en{c}_1.$$

(2)

Ideally, $∆s_0$ and $∆s_1$ correspond to the lateral and longitudinal displacement increments in the vehicle frame. If installation non-orthogonality exists, an auxiliary odometry coordinate frame is used for calibration. For a small non-orthogonal deviation $\alpha$, the corrected vehicle-frame displacement increment can be expressed as:

$$∆p_b=\left[\begin{array}{c}∆x_b\\ ∆y_b\end{array}\right]=C_{\alpha }\left[\begin{array}{c}∆s_0\\ ∆s_1\end{array}\right],$$

(3)

where $C_{\alpha }$ is the calibration matrix determined from the measured installation angle and distance calibration experiments.

2.3. Hardware Platform and Embedded Implementation

2.3.1. Main Controller, Power Supply, and Motor Drive

The embedded control system uses an Infineon TRAVEO CYT4BB77 microcontroller with Arm Cortex-M4 and Cortex-M0+ cores and a maximum operating frequency of 350 MHz. The controller executes multi-task processing for sensor acquisition, attitude estimation, planar localization, velocity mapping, and closed-loop motor control. The prototype is powered by a 6S lithium battery pack with a nominal voltage of 22.2 V and a full-charge voltage of 25.2 V. As shown in Figure 2, the 6S LiPo battery supplies the motor drivers and chassis motors through the 22.2 V high-voltage path. A DC-DC buck converter provides regulated 3.3 V power for the orthogonal passive-wheel odometry encoders, IMU/gyroscope, magnetometer, and gimbal sensors.

The motor drive uses TI DRV8701E H-bridge gate drivers for DC brushed motors. The DRV8701E supports 100% duty-cycle operation and can be controlled through PWM and direction logic. Four independent drive circuits are used for the four Mecanum wheels. Current sensing and overcurrent protection are included to improve safety during start-up, emergency stops, and high-load following.

2.3.2. Attitude Sensing and Human–Machine Interface

The attitude sensing module uses Bosch BMI270 and STMicroelectronics LSM6DSRTR six-axis IMUs. The BMI270 provides gyroscope and accelerometer data suitable for motion-state perception. The LSM6DSRTR provides low-noise inertial data for stable attitude estimation. Both sensors communicate with the main controller through standard embedded interfaces. The platform also includes an IPS200 or serial display interface for showing heading, planar coordinates, gimbal posture, velocity commands, and operating mode.

2.3.3. Software Architecture

The software follows a layered data-flow architecture:

• Sensor acquisition: reads IMU data and encoder pulse increments.
• Error compensation: performs zero-bias compensation, noise filtering, temperature-drift compensation, and static-state suppression.
• Attitude estimation: updates the quaternion attitude and converts it to Euler angles.
• Coordinate calculation: estimates planar displacement and heading in the navigation coordinate frame.
• Velocity mapping: converts gimbal posture to target chassis velocity.
• Motion control: generates wheel velocity commands and feedback correction.
• Display and parameter interface: shows system status and allows parameter adjustment.

This modular structure separates low-level sensor handling from high-level following control. It also allows the same platform to switch between fixed-point planar motion and gimbal-based passive following.

2.4. Coordinate Frames and Kinematic Modeling

Four coordinate frames are defined:

• Navigation frame $n$: a fixed East-North-Up reference frame. The initial platform position is defined as the origin.
• Vehicle frame $b$: a body-fixed frame whose origin is located at the geometric center of the chassis. The $x_b$ axis points to the right side of the chassis, the $y_b$ axis points forward, and the $z_b$ axis points upward.
• Gimbal frame $g$: a frame fixed to the gimbal top. Pitch and roll relative to the vehicle frame represent traction intention.
• Odometry frame $o$: a planar frame associated with the orthogonal passive wheels.

Figure 4 contains a physical view of the orthogonal passive-wheel odometry module and a coordinate schematic for planar dead reckoning. The two passive omni wheels have a diameter of 65 mm and are theoretically mounted with a 90-degree included angle, so the two wheels measure two vehicle-frame displacement components. Magnetic encoders measure the rotation of the passive wheels. Any small installation non-orthogonality is represented by alpha and compensated by the calibration matrix $C_{alpha}$ before the vehicle-frame displacement increment is rotated into the navigation frame by the heading angle psi.

After orthogonal odometry provides the vehicle-frame displacement increment $∆p_b$, the navigation-frame displacement increment is calculated using the platform heading $\psi$:

$$\left[\begin{array}{c}∆x_n\\ ∆y_n\end{array}\right]=\left[\begin{array}{cc}\mathrm{c}\mathrm{o}\mathrm{s} \psi & -\mathrm{s}\mathrm{i}\mathrm{n} \psi \\ \mathrm{s}\mathrm{i}\mathrm{n} \psi & \mathrm{c}\mathrm{o}\mathrm{s} \psi \end{array}\right]\left[\begin{array}{c}∆x_b\\ ∆y_b\end{array}\right].$$

(4)

The planar position is then recursively updated:

$$x_n\left(k\right)=x_n\left(k-1\right)+∆x_n\left(k\right),$$

(5)

$$y_n\left(k\right)=y_n\left(k-1\right)+∆y_n\left(k\right).$$

(6)

The inverse kinematics of a four-Mecanum-wheel chassis can be written in the general form:

$$\mathit{\omega }={\displaystyle \frac{1}{r}}J\left[\begin{array}{c}{v}_x\\ v_y\\ {\omega }_z\end{array}\right],$$

(7)

where $r$ is the Mecanum-wheel radius, $\mathit{\omega }$ is the four-wheel angular velocity vector, $\left(v_x,v_y\right)$ are vehicle-frame translational velocities, ${\omega }_z$ is the yaw angular velocity, and $J$ is determined by the wheel arrangement and chassis geometry. In this study, the following system focuses on generating $v_x$ and $v_y$ from the gimbal posture, while ${\omega }_z$ is controlled by the platform heading and task mode.

2.5. Posture-to-Velocity Mapping

The gimbal pitch angle $\theta$ is mapped to the forward-backward velocity command $v_y$, and the roll angle $\varphi$ is mapped to the lateral velocity command $v_x$. The mapping is designed to be sensitive near intentional pulling, stable near zero, and bounded at high deflection angles.

For the pitch axis:

$$v_y\left(\theta \right)=\left\{\begin{array}{cc}0,& \left|\theta \right|<{\theta }_{dead},\\ k_{\theta }·\mathrm{s}\mathrm{g}\mathrm{n}\left(\theta \right)\left(\left|\theta \right|-{\theta }_{dead}\right),& {\theta }_{dead}\le \left|\theta \right|<{\theta }_{sat},\\ \mathrm{s}\mathrm{g}\mathrm{n}\left(\theta \right)v_{y,max},& \left|\theta \right|\ge {\theta }_{sat}.\end{array}\right.$$

(8)

The roll-axis mapping uses the same form:

$$v_x\left(\varphi \right)=\left\{\begin{array}{cc}0,& \left|\varphi \right|<{\varphi }_{dead},\\ k_{\varphi }·\mathrm{s}\mathrm{g}\mathrm{n}\left(\varphi \right)\left(\left|\varphi \right|-{\varphi }_{dead}\right),& {\varphi }_{dead}\le \left|\varphi \right|<{\varphi }_{sat},\\ \mathrm{s}\mathrm{g}\mathrm{n}\left(\varphi \right)v_{x,max},& \left|\varphi \right|\ge {\varphi }_{sat}.\end{array}\right.$$

(9)

The implemented parameters are ${\theta }_{dead}={\varphi }_{dead}=2$ deg, $k_{\theta }=k_{\varphi }=15$ mm/s/deg, ${\theta }_{sat}={\varphi }_{sat}=15$ deg, and $v_{x,max}=v_{y,max}=500$ mm/s. A first-order low-pass filter is applied to suppress sudden velocity jumps:

$$G\left(s\right)={\displaystyle \frac{1}{\tau s+1}},$$

(10)

where $\tau =0.1$ s. In addition, acceleration limiting constrains the velocity command variation per control cycle:

$$\left|v_i\left(k\right)-v_i\left(k-1\right)\right|\le a_{max}∆t,i\in \left\{x,y\right\}.$$

(11)

The final target velocity is:

$$v_{cmd}=\left[\begin{array}{c}{v}_x\\ v_y\end{array}\right].$$

(12)

This mapping transforms the user’s continuous traction action into smooth omnidirectional motion commands.

The mapping process can be interpreted as five sequential steps. First, small deflections within the dead zone are ignored to prevent unintended motion. Second, the effective pitch and roll deflections beyond the dead zone are converted into longitudinal and lateral velocity components through a linear gain. Third, the raw velocity command is bounded by the software command limit. Fourth, the command is smoothed using a first-order low-pass filter. Fifth, the velocity variation between consecutive control cycles is constrained by acceleration limiting.

It should be noted that the velocity generated by the linear posture-to-velocity mapping and the final software command limit are two different quantities. With the implemented parameters, namely θ_dead = ϕ_dead = 2 deg, $k_{\mathsf{\theta }}=k_{\mathsf{\varphi }}=15 \mathrm{mm}/\mathrm{s}/\mathrm{deg},$ and ${\mathsf{\theta }}_{\mathrm{sat}}={\mathsf{\varphi }}_{\mathrm{sat}}={15}^{\circ }$, the maximum value generated by the linear branch at the saturation angle is 15 × (15 − 2) = 195 mm/s. Therefore, v_xmax = v_ymax = 500 mm/s denotes the upper software limit applied to the final velocity command, rather than the velocity value generated exactly at theta_sat = 15 deg.

The 600 mm/s condition used in the traction-speed tests refers to the externally imposed traction-speed level over the 5000 mm test path. It is not the platform velocity command limit. Thus, the 600 mm/s traction-speed condition and the 500 mm/s platform command limit represent two different physical quantities.

2.6. Attitude Estimation and Gyroscope Error Compensation

The gimbal attitude is estimated from gyroscope and accelerometer data. Quaternion representation is used to avoid singularities associated with Euler-angle integration. Let the quaternion be:

$$q=[q_0,q_1,q_2,q_3{]}^T.$$

(13)

The quaternion derivative driven by angular velocity $\omega =[{\omega }_x,{\omega }_y,{\omega }_z{]}^T$ is:

$$\dot{q}={\displaystyle \frac{1}{2}}\Omega \left(\mathit{\omega }\right)q,$$

(14)

where

$$\Omega \left(\mathit{\omega }\right)=\left[\begin{array}{cccc}0& -{\omega }_x& -{\omega }_y& -{\omega }_z\\ {\omega }_x& 0& {\omega }_z& -{\omega }_y\\ {\omega }_y& -{\omega }_z& 0& {\omega }_x\\ {\omega }_z& {\omega }_y& -{\omega }_x& 0\end{array}\right].$$

(15)

The quaternion is updated numerically and normalized at each cycle. Euler angles are then obtained for the posture-to-velocity mapping. To improve long-term stability, the following compensation steps are applied:

• Static zero-bias compensation for gyroscope output.
• Kalman filtering or complementary filtering for noise suppression.
• Temperature drift compensation using calibration data.
• Static-state thresholding to suppress small residual angular velocity accumulation.

The system compares gradient-descent attitude estimation and Mahony complementary filtering. The final compensated scheme combines filtering, temperature drift compensation, and constant zero-bias compensation.

2.7. Closed-Loop Passive Following Control

The following two modes are considered. Mode A is an open-loop attitude following: the platform receives velocity commands generated only from the gimbal posture mapping. Mode B is closed-loop following: the platform uses orthogonal odometry localization feedback to correct accumulated displacement and reduce path deviation.

Let $p_{ref}$ be the desired endpoint or trajectory state inferred from the traction command and $p$ be the estimated platform position from orthogonal odometry. A simple feedback correction can be written as:

$$v_{ref}=v_{cmd}+K_p\left(p_{ref}-p\right),$$

(16)

where $K_p$ is the planar correction gain. In continuous following, the feedback term is limited to avoid overriding the user’s direct traction intention. The purpose of the closed loop is not autonomous navigation but reduction in drift, overshoot, and accumulated following error. The closed-loop controller should be interpreted as a bounded proportional correction superimposed on the gimbal-generated velocity command.

The main motion-control loop was executed at 100 Hz, corresponding to a sampling period of 0.01 s. The IMU attitude update rate was set to 200 Hz, while the orthogonal odometry and closed-loop position correction were updated at 100 Hz. The motor PWM frequency was set to 20 kHz to ensure smooth DC motor driving.

The planar feedback gain was selected as $\left(K_{px}=K_{py}=0.8 {\mathrm{s}}^{-1}\right)$. With this setting, a 100 mm planar position error produces an 80 mm/s correction velocity before saturation. To prevent the closed-loop correction from overriding the user’s direct traction intention, the feedback correction velocity was limited to 120 mm/s, which is 24% of the maximum software velocity command. The acceleration limit was set to $\left(1000{ \mathrm{mm}/\mathrm{s}}^2\right)$, so that the platform could reach the maximum command velocity of 500 mm/s within approximately 0.5 s under continuous traction input.

2.8. Experimental Protocol and Evaluation Metrics

Experiments were conducted on indoor flat ground. Unless otherwise stated, each test was repeated five times, and the mean value or mean +/− standard deviation was recorded.

In the linear displacement tests, the reference displacement was determined from the commanded reference distance and verified using an external calibration ruler or magnetic scale placed along the test direction. For the square and circular trajectory tests, the expected trajectories were generated from preset geometric paths, whereas the actual trajectories were reconstructed from the orthogonal odometry fusion output. The start and end points are explicitly indicated in Figure 5 and Figure 6.

For the square trajectory test, a fixed-size aluminum-profile frame was used as the physical reference structure to constrain and verify the prescribed square path. For the circular trajectory test, an aluminum-profile support with a fixed center height and a fixed radius was used to define the reference circular path.

2.8.1. Attitude Estimation Accuracy

The gimbal was mounted on a calibration rotation platform and rotated about pitch and roll axes at angular velocities of 10 deg/s, 30 deg/s, and 60 deg/s. Reference angles were provided by the rotation platform. Dynamic tracking error and root mean square error (RMSE) were used:

$${ϵ}_{dyn}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\left|{\widehat{\theta }}_i-{\theta }_{ref,i}\right|,$$

(17)

$${ϵ}_{RMSE}=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N({\widehat{\theta }}_i-{\theta }_{ref,i}{)}^2}.$$

(18)

Static bias was measured by holding the gimbal stationary and recording the attitude output.

2.8.2. Planar Localization Accuracy

The platform was commanded to translate along the $x_n$ and $y_n$ axes over distances of 1000 mm, 2000 mm, and 3000 mm. A calibration ruler or magnetic scale was used as the reference. Turning tests used commanded angles of 90 deg, 180 deg, and 360 deg. Composite trajectories included a square trajectory with a side length of 2000 mm and a circular trajectory with a radius of 1000 mm.

2.8.3. Passive Following Performance

The user pulled the platform through forward, lateral, and 45 deg diagonal trajectories over 5000 mm. Traction speeds were divided into low speed (200 mm/s), medium speed (400 mm/s), and high speed (600 mm/s). Evaluation metrics included the following: distance error, response time, average trajectory offset, and steady-state following error.

2.8.4. Comparative Experiments

Three comparative experiments were performed:

• Pure Mecanum-wheel drive odometry versus orthogonal odometry fusion.
• Uncompensated gyroscope integration, Kalman filtering only, and full compensation.
• Open-loop attitude following versus closed-loop following with orthogonal odometry feedback.

2.8.5. Statistical Analysis

To improve the reliability of the experimental evaluation, each test was repeated five times unless otherwise stated. The experimental results are reported as mean values and standard deviations. The mean value was used to describe the average performance of each method or test condition, while the standard deviation was used to evaluate the repeatability and dispersion of repeated measurements.

Because the present study focuses on prototype-level engineering validation and the number of repeated trials is limited, the statistical treatment is mainly descriptive. Therefore, the comparison between different methods is based on the reported mean error, standard deviation, maximum error, relative error, and percentage improvement. Inferential statistical tests, such as confidence-interval analysis or hypothesis testing, will be further introduced in future work when larger-scale repeated experiments and complete raw measurement datasets are available.

3. Results

3.1. Attitude Estimation Performance

The compensated attitude estimation module maintained stable outputs under static and dynamic conditions. In the static test, the pitch-axis static bias was 0.028 deg, the roll-axis static bias was 0.026 deg, and the yaw static drift rate after full compensation was 0.45 deg/h.

Table 1. Attitude estimation errors at different angular velocities.

Rotation Axis	Angular Velocity (deg/s)	Dynamic Tracking Error (deg)	RMSE (deg)
Pitch	10	0.23	0.31
Pitch	30	0.35	0.42
Pitch	60	0.48	0.56
Roll	10	0.21	0.29
Roll	30	0.32	0.39
Roll	60	0.44	0.52

summarizes dynamic tracking performance at different angular velocities.

The RMSE increased slightly as angular velocity increased, but remained below 0.56 deg in all tested cases. This accuracy is sufficient for the posture-to-velocity mapping because the dead-zone threshold is 2 deg. The attitude noise therefore remains well below the level required to trigger unintended platform motion.

3.2. Planar Localization Accuracy

The orthogonal odometry fusion module achieved millimeter-level error in short-range indoor tests.

Table 2. Linear positioning test results using orthogonal odometry fusion.

Motion Direction	Set Distance (mm)	Average Output Distance (mm)	Average Error (mm)	Max Error (mm)	Relative Error (%)
X-axis positive	1000	1001.2	1.2	2.1	0.12
X-axis positive	2000	2002.8	2.8	3.9	0.14
X-axis positive	3000	3003.5	3.5	4.8	0.12
Y-axis positive	1000	999.4	0.6	1.5	0.06
Y-axis positive	2000	1998.7	1.3	2.4	0.07
Y-axis positive	3000	2996.2	3.8	5.2	0.13

shows linear positioning results along the $x_n$ and $y_n$ axes.

For 3000 mm translation, the average errors were 3.5 mm along the X axis and 3.8 mm along the Y axis, corresponding to relative errors of 0.12% and 0.13%, respectively. Turning-positioning tests are summarized in

Table 3. Turning-positioning test results.

Set Angle (deg)	Average Output Angle (deg)	Average Error (deg)	Max Error (deg)	Relative Error (%)
90	89.79	0.21	0.35	0.23
180	179.58	0.42	0.58	0.23
360	359.52	0.48	0.72	0.13

.

The average angular error was below 0.5 deg even for 360 deg rotation. The results indicate that the fused localization method provides a stable pose reference for closed-loop following.

Composite trajectory results further confirm the improvement after non-orthogonal correction. The measured angle between the two passive wheels was 89.72 deg, corresponding to a non-orthogonal deviation of 0.28 deg.

Table 4. Comparison of positioning accuracy before and after non-orthogonal correction.

Test Item	Average Error Before Correction	Average Error After Correction	Accuracy Improvement
X-axis linear 3000 mm	9.6 mm	3.5 mm	63.5%
Y-axis linear 3000 mm	8.9 mm	3.8 mm	57.3%
Square trajectory closed loop	28.4 mm	12.3 mm	56.7%

compares positioning errors before and after correction.

In Figure 5, the black marker denotes the preset start point, and the red marker denotes the measured endpoint. The yellow curve is the expected square trajectory generated from the preset path geometry, and the blue curve is the trajectory estimated from the odometry fusion output during user-guided traction.

In Figure 6, the black marker denotes the preset start point, and the red marker denotes the measured endpoint. The expected circular trajectory was generated from the preset radius and center, while the actual trajectory was reconstructed from the fused odometry estimate.

3.3. Passive Following Performance

Forward, lateral, and diagonal following tests were conducted over a 5000 mm distance.

Table 5. Forward traction following test results.

Traction Speed	Following Distance Error (mm)	Following Response Time (s)	Average Trajectory Offset (mm)	Steady-State Following Error (mm)
Low speed (200 mm/s)	6.2 +/− 2.1	0.18 +/− 0.03	4.8 +/− 1.2	15.3 +/− 3.5
Medium speed (400 mm/s)	11.5 +/− 3.4	0.15 +/− 0.02	9.6 +/− 2.3	23.7 +/− 4.8
High speed (600 mm/s)	18.6 +/− 4.2	0.12 +/− 0.02	15.2 +/− 3.1	32.1 +/− 5.6

presents forward traction results.

The response time decreased as the traction speed increased because higher gimbal deflection exceeded the dead zone more rapidly. The following distance error increased with speed, which is consistent with stronger acceleration and larger inertial effects at high traction speed.

Table 6. Lateral traction following test results.

Traction Speed	Following Distance Error (mm)	Following Response Time (s)	Average Trajectory Offset (mm)	Steady-State Following Error (mm)
Low speed (200 mm/s)	8.3 +/− 2.8	0.19 +/− 0.04	6.5 +/− 1.8	18.6 +/− 4.2
Medium speed (400 mm/s)	14.2 +/− 3.9	0.16 +/− 0.03	12.4 +/− 2.9	28.5 +/− 5.3
High speed (600 mm/s)	21.4 +/− 5.1	0.13 +/− 0.03	18.7 +/− 3.8	38.2 +/− 6.8

shows lateral traction results.

Lateral following errors were slightly larger than forward following errors. This is expected because lateral Mecanum motion is more sensitive to roller-ground contact variation and load distribution.

Table 7. Diagonal 45 deg traction following test results.

Traction Speed	Following Distance Error (mm)	Following Response Time (s)	Average Trajectory Offset (mm)	Steady-State Following Error (mm)
Low speed (200 mm/s)	11.2 +/− 3.5	0.21 +/− 0.04	9.8 +/− 2.5	24.3 +/− 5.1
Medium speed (400 mm/s)	18.5 +/− 4.6	0.17 +/− 0.03	16.3 +/− 3.6	34.8 +/− 6.4
High speed (600 mm/s)	26.3 +/− 5.8	0.14 +/− 0.03	23.4 +/− 4.5	45.6 +/− 7.9

presents diagonal 45 deg traction results.

The diagonal following produced the largest errors among the three tested directions because both lateral and longitudinal velocity components were active simultaneously. Even in this condition, the average distance error remained below 30 mm at 600 mm/s over a 5000 mm trajectory.

3.4. Comparative Results

3.4.1. Pure Mecanum-Wheel Odometry Versus Orthogonal Odometry Fusion

Table 8. Comparison of linear motion positioning accuracy over 3000 mm.

Scheme	Average Error (mm)	Max Error (mm)	Standard Deviation (mm)	Relative Error (%)
Pure Mecanum-wheel odometry	24.6	38.2	6.3	0.82
Orthogonal odometry fusion	3.8	5.2	1.1	0.13

compares pure drive-wheel odometry and orthogonal odometry fusion over a 3000 mm X-axis motion.

The orthogonal odometry fusion method reduced the average error from 24.6 mm to 3.8 mm, an improvement of approximately 84.6%. In circular motion, the pure Mecanum-wheel scheme produced an average closed-loop error of 42.5 mm and a maximum error of 58.6 mm, while orthogonal odometry fusion reduced these values to 11.2 mm and 15.8 mm. In repeated start-stop motion over 3000 mm, pure Mecanum-wheel odometry accumulated 35.2 mm error, whereas orthogonal odometry fusion accumulated 4.6 mm.

The comparison results show that the orthogonal odometry fusion method produced lower positioning errors than pure Mecanum-wheel odometry in the repeated tests. The improvement is reflected by reductions in mean error, maximum error, standard deviation, and relative error.

3.4.2. Effect of Gyroscope Compensation

Table 9. Performance comparison before and after gyroscope compensation.

Metric	Uncompensated	Kalman Filtering Only	Full Compensation
Static yaw drift (deg/h)	12.3	3.8	0.45
Linear positioning closed-loop error (mm)	45.6	18.3	5.2
Circular trajectory positioning error (mm)	52.8	22.6	8.4
Attitude estimation RMSE (deg)	1.52	0.68	0.23

compares uncompensated integration, Kalman filtering only, and full compensation.

Full compensation reduced static yaw drift by 96.3% relative to uncompensated integration and reduced attitude RMSE from 1.52 deg to 0.23 deg. Because heading enters the coordinate transformation from the vehicle frame to the navigation frame, gyroscope compensation also improved planar localization.

3.4.3. Open-Loop Versus Closed-Loop Following

Table 10. Comparison of the following performance with and without the localization closed loop.

Control Mode	Following Distance Error (mm)	Max Error (mm)	Standard Deviation (mm)	Average Trajectory Offset (mm)
Open-loop mode	38.6	62.4	12.8	32.5
Closed-loop mode	11.5	18.6	3.4	9.6

compares open-loop attitude following with closed-loop following using orthogonal odometry feedback.

Closed-loop following reduced the average following distance error by approximately 70.2% and reduced the average trajectory offset by approximately 70.5%. In the start-stop response test, open-loop mode produced an average stopping overshoot of 45.3 mm and required 1.2 s to stabilize. Closed-loop mode reduced overshoot to 12.6 mm and stabilized within 0.4 s.

The comparison results indicate that the closed-loop method reduced both the following distance error and the trajectory offset compared with the open-loop method. The lower mean error and standard deviation suggest that orthogonal odometry feedback improves following accuracy and repeatability.

4. Discussion

4.1. Significance of Orthogonal Passive-Wheel Odometry for Mecanum Platforms

The results show that orthogonal passive-wheel odometry is effective for improving planar localization on a Mecanum-wheel platform. Pure drive-wheel odometry is vulnerable to the same physical mechanism that gives Mecanum wheels their omnidirectional capability: roller-ground contact. During acceleration, lateral motion, diagonal motion, and start-stop cycles, drive-wheel encoder pulses do not always represent actual platform displacement. The experimental comparison in Table 8 confirms this effect: pure Mecanum-wheel odometry produced a 24.6 mm average error over a 3000 mm trajectory, while orthogonal odometry fusion reduced the error to 3.8 mm.

The orthogonal passive wheels decouple measurement from propulsion. Their function is to roll with actual chassis displacement rather than generate driving force. Therefore, they provide a more direct measurement of planar displacement. The remaining error sources are mainly passive-wheel radius error, encoder quantization, installation non-orthogonality, ground contact quality, and heading estimation error. These errors are easier to calibrate than the Mecanum drive slip because they are less dependent on transient motor torque and roller contact state.

The non-orthogonal correction results in Table 4 further demonstrate that mechanical installation error must be included in the model. A measured 0.28 deg angle deviation between passive-wheel axes increased position and trajectory errors, while auxiliary coordinate correction reduced the square trajectory closed-loop error from 28.4 mm to 12.3 mm. This supports the use of mechanical calibration and coordinate compensation as part of the localization module.

4.2. Naturalness and Robustness of Gimbal Posture Interaction

The gimbal posture interface provides a simple physical channel for user intention. When a user pulls the rope forward, the gimbal pitch changes; when the user pulls laterally, the roll angle changes. This creates a direct mapping between a natural pulling action and the robot’s planar motion. Unlike button control, the mapping is continuous and does not require the user to combine discrete commands for diagonal or curved motion. Unlike vision-based following, the interaction remains available under lighting changes, occlusion, and low-texture environments.

The posture-to-velocity mapping is intentionally simple. Dead-zone processing suppresses unintended motion caused by small hand tremor and sensor noise. Saturation prevents excessive speed under large gimbal deflection. Low-pass filtering and acceleration limiting reduce abrupt command changes. The experimental results show that this design achieves response times of 0.12–0.21 s depending on traction direction and speed, while maintaining trajectory offsets within tens of millimeters over 5000 mm tasks.

Compared with force-sensing handles or admittance-controlled mobile bases, the proposed interface measures posture rather than force. This choice lowers sensing complexity and avoids the need for calibrated multi-axis force sensors. However, it also means that the mapping parameters depend on rope length, gimbal stiffness, installation height, and user posture. This trade-off is acceptable for a compact companion platform, but future work should include adaptive parameter identification to improve consistency across users.

Compared with joystick control, the gimbal-rope interface preserves the physical metaphor of pulling a cart and naturally supports diagonal motion through simultaneous pitch and roll deflection. Compared with force-sensing handles, it reduces sensor complexity by using posture rather than calibrated multi-axis force. Compared with general omnidirectional platforms, the contribution of the present system is the integration of a physical traction interface with independent passive-wheel localization feedback. These advantages are practical rather than universal: joystick control may remain preferable when precise discrete commands are required, and force/admittance interfaces may be preferable when actual interaction force must be measured.

4.3. Closed-Loop Following as the Link Between Intention and Motion Accuracy

Gimbal posture alone can identify user intention, but cannot guarantee accurate platform pose. Orthogonal odometry feedback closes this gap by providing a planar localization reference. The comparison in Table 10 shows that closed-loop feedback substantially reduces following error and trajectory offset. This indicates that the system should not treat interaction sensing and localization as separate modules. Instead, physical intention perception should generate the desired motion, and independent localization should correct the realized motion.

The same principle explains the improvement observed after gyroscope compensation. Heading error enters the coordinate transformation from vehicle-frame displacement to navigation-frame displacement. If yaw drift is not compensated, even accurate passive-wheel displacement increments can be projected into the wrong global direction. Full compensation reduced yaw drift from 12.3 deg/h to 0.45 deg/h and improved both attitude RMSE and planar trajectory accuracy.

4.4. Engineering Application Scenarios

The proposed system is suitable for application scenarios where the operator remains near the platform, and direct physical guidance is acceptable or preferred. In medical and rehabilitation settings, a rope-guided omnidirectional platform can act as a companion cart or lightweight transport base. In warehouses, laboratories, and factories, it can assist with manual material movement where a worker wants a mobile base to follow without requiring visual tracking or infrastructure. In exhibition halls, airports, and hotels, direct physical control can be safer and more predictable than fully autonomous following in dense pedestrian environments.

Example operating scenarios include a rehabilitation cart following a therapist along a bedside corridor, a laboratory trolley carrying instruments beside an operator, a warehouse picking cart moving between shelves, and a hotel or exhibition service platform moving under close human supervision. In each case, the operator remains near the platform, and the desired behavior is physically guided following rather than independent path planning.

The method may also be useful in special low-perception-dependence scenarios. For example, in a tethered air–ground cooperative setup, an aerial or external operator could provide physical guidance while the ground Mecanum platform performs precise planar movement. In such use cases, the main benefit is not full autonomy but robust motion under limited perception.

4.5. Limitations

Several limitations remain. First, the gimbal posture-to-velocity mapping parameters are currently fixed. Rope length, gimbal installation height, user height, and mechanical stiffness can change the relationship between pulling force and posture angle. Second, aggressive pulling can cause overshoot or oscillation. Although filtering and acceleration limiting reduce abrupt motion, a more systematic admittance-like dynamic model may improve comfort and stability. Third, the experiments were conducted mainly on indoor flat ground with a limited number of operators and predefined speeds. Performance under carpet, tile gaps, ramps, slopes, uneven surfaces, and long-term operation requires further validation. Finally, the present system provides relative localization; long-distance operation may still require external references or loop correction.

In addition, the current prototype does not include AI-based task planning or semantic scene understanding. Such functions could be added as an upper-level planning layer in future work, but they are outside the scope of this study, which focuses on the lower-level interaction, localization, and motion-control chain. The compact rectangular chassis is also a prototype choice; practical deployment in complex internal workspaces would require enclosure design, edge protection, payload-specific stability analysis, and additional obstacle-safety measures.

5. Conclusions

This paper proposed and experimentally validated a passive following system for a Mecanum-wheel mobile platform based on gimbal posture perception and orthogonal odometry fusion. A rope-tensioned gimbal with a top-mounted six-axis IMU was used to capture user traction intention through pitch and roll angles. A piecewise posture-to-velocity mapping model converted the gimbal attitude into smooth omnidirectional velocity commands. Orthogonal passive-wheel odometry and inertial attitude estimation provided planar localization feedback independent of the Mecanum drive wheels.

Experimental results demonstrate that the system achieves accurate attitude estimation, high-precision planar localization, and stable passive following. Full gyroscope compensation reduced static yaw drift to 0.45 deg/h and attitude RMSE to 0.23 deg in the tested condition. Orthogonal odometry fusion reduced the average 3000 mm linear positioning error from 24.6 mm with pure Mecanum-wheel odometry to 3.8 mm. Closed-loop following reduced average distance error from 38.6 mm to 11.5 mm compared with open-loop attitude mapping. These results indicate that combining physical gimbal interaction with independent orthogonal odometry feedback can improve both naturalness and accuracy in low-perception-dependence indoor following tasks.

Future work will focus on adaptive mapping parameter identification, more robust anti-overshoot control under aggressive pulling, longer-duration field tests with multiple users, higher-quality mechanical packaging, and integration with optional external localization references for larger-scale deployment.