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Machines
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Motion Planning and Control in Autonomous Robotic Systems
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Motion Planning and Control in Autonomous Robotic Systems

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Automation and Control Systems".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 1445

Editors

Prof. Dr. Wei Sun

E-Mail Website
Guest Editor
School of Mathematics Science, Liaocheng University, Liaocheng 252000, China
Interests: nonlinear system control; adaptive control; robotics control; flexible joint; event-triggered control; underactuated mechanical systems
Dr. Tong Yang

E-Mail Website
Guest Editor
Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin 300350, China
Interests: motion control; robot control; motion/trajectory planning; dynamics analysis and control of underactuated systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As robotics enters a new era of high intelligence and autonomy, the complex dynamic characteristics exhibited by these systems place higher demands on control theory. Modern robots are not merely assemblies of mechanical structures but are deeply coupled nonlinear systems operating in dynamic environments filled with uncertainties.

This Special Issue aims to explore the deep integration of intelligent algorithms and nonlinear control theory in the field of robotics. We focus on leveraging advanced mathematical modeling, intelligent perception, and control strategies to enhance the motion precision, operational flexibility, and environmental adaptability of robotic systems. We cordially invite researchers to share innovative achievements in nonlinear control, system optimization, and control scheme design under complex working conditions. Potential topics for this Special Issue include, but are not limited to:

  • Advanced Nonlinear Control Architectures: Control design and analysis for multi-degree-of-freedom or flexible structures.
  • Intelligent Control Methodologies: Strategies to improve environmental adaptability and autonomous decision-making.
  • Novel Modeling and Representation Schemes: High-order modeling and control-oriented models based on the fundamental physical structure of robot dynamics.
  • Motion Planning and Dynamic Optimization: Path generation, obstacle avoidance, and optimal control strategies under complex constraints.
  • Efficient Control under Resource Constraints: Triggered control mechanisms for systems with limited communication bandwidth or computational resources.
  • Collaborative and Swarm Intelligence: Coordination, synchronization, and collective control logic for multi-robot systems.

Prof. Dr. Wei Sun
Dr. Tong Yang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • motion planning
  • intelligent control
  • robotic system
  • dynamic optimization
  • nonlinear control

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Published Papers (4 papers)

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Research

19 pages, 1845 KB  
Article
A Hierarchical Shared Steering Control Strategy Based on Driver States
by Quanjin Wang, Lina Xuan, Jiwei Feng and Jian Wu
Machines 2026, 14(8), 837; https://doi.org/10.3390/machines14080837 - 23 Jul 2026
Viewed by 184
Abstract
Continuous shared control provides an effective approach for intelligent vehicles to balance driving autonomy and system safety boundaries in complex human–machine interaction scenarios. However, existing shared control methods fail to dynamically adapt to the complex and time-varying states of the driver. To address [...] Read more.
Continuous shared control provides an effective approach for intelligent vehicles to balance driving autonomy and system safety boundaries in complex human–machine interaction scenarios. However, existing shared control methods fail to dynamically adapt to the complex and time-varying states of the driver. To address this limitation, a hierarchical shared steering control strategy based on driver states is proposed in this paper. First, an in-vehicle eye tracker is utilized to collect data, and recognition features are extracted based on real-world datasets. Subsequently, a CNN-TCN deep learning algorithm is employed to train a model for identifying five-dimensional driver states. To mitigate excessive intervention and driving experience degradation caused by model misclassifications, a total probability weighting mechanism is developed. This mechanism integrates the real-time confidence distribution output by the neural network with the established baseline safety weights for each driving state, enabling the dynamic and continuous computation of the initial machine control authority. Furthermore, to eliminate high-frequency confidence spikes at the state perception end, a weight-smoothing strategy is designed using an adaptive nonlinear tracking differentiator based on Active Disturbance Rejection Control (ADRC). An autonomous driving controller is then constructed using the Linear Quadratic Regulator (LQR) method to ensure vehicle stability. Finally, Hardware-in-the-Loop (HIL) experiments conducted on a human–machine driving platform with hardware feedback verify the feasibility and superiority of the proposed method. Full article
(This article belongs to the Special Issue Motion Planning and Control in Autonomous Robotic Systems)
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27 pages, 535 KB  
Article
Robust Adaptive Cooperative Tracking Control for Multi-Train Systems with State Constraints, Collision Avoidance, and Time-Varying Parametric Uncertainties
by Yi Huang, Zuguo Chen, Chaoyang Chen and Biao Luo
Machines 2026, 14(7), 828; https://doi.org/10.3390/machines14070828 - 21 Jul 2026
Viewed by 161
Abstract
This paper investigates cooperative tracking control for virtually coupled multi-train systems subject to nonlinear running resistance, bounded time-varying resistance parameters, state constraints, and actuator saturation. The theoretical contribution is not the separate use of barrier Lyapunov functions, adaptive control, anti-windup compensation, or distributed [...] Read more.
This paper investigates cooperative tracking control for virtually coupled multi-train systems subject to nonlinear running resistance, bounded time-varying resistance parameters, state constraints, and actuator saturation. The theoretical contribution is not the separate use of barrier Lyapunov functions, adaptive control, anti-windup compensation, or distributed cooperative control. Instead, the revised analysis establishes a coupled safety-and-boundedness certificate for the actual saturated closed-loop vector field. The closing-speed-aware spacing variable and actuator-authority condition support a first-exit proof of forward invariance, after which a composite Lyapunov analysis couples the saturation residual, anti-windup state, cooperative tracking error, and time-varying parameter-estimation error to establish uniform ultimate boundedness without persistent excitation. This proof architecture distinguishes the proposed controller from recent constrained train-control methods focused separately on velocity/input bounds, distance-oriented full-state barriers, or iteration-indexed learning. Numerical studies with heterogeneous trains, stronger time-varying aerodynamic perturbations, normalized actuator limits, tracking-bound verification, constrained baselines, a near-boundary safety-allocation case, and a quantitative one-factor-at-a-time parameter-sensitivity study are provided. Full article
(This article belongs to the Special Issue Motion Planning and Control in Autonomous Robotic Systems)
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22 pages, 4028 KB  
Article
Closed-Form Quintic B-Spline Reconstruction via Higher-Order Derivative Degeneration for Trajectory Smoothing
by Zhenyu Yin, Song Li, Heran Wang, Huixuan Zhu, Liming Zhang, Feiyang Gao and Xiongfei Zheng
Machines 2026, 14(7), 785; https://doi.org/10.3390/machines14070785 - 13 Jul 2026
Viewed by 228
Abstract
In industrial trajectory planning and real-time motion control, quintic B-splines are widely used for corner smoothing owing to their local support and high-order continuity. However, existing evaluation methods mainly rely on basis-function recursion or the de Boor algorithm, with limited attention paid to [...] Read more.
In industrial trajectory planning and real-time motion control, quintic B-splines are widely used for corner smoothing owing to their local support and high-order continuity. However, existing evaluation methods mainly rely on basis-function recursion or the de Boor algorithm, with limited attention paid to the analytical properties of fixed-topology continuity-constrained structures. This study reveals that, under geometric symmetry and C3 continuity constraints at the junction points, higher-order derivative control-point structures undergo progressive geometric degeneration, whereby second- and third-order derivatives reduce to one-dimensional forms governed by a single direction. Based on this degeneration property, a closed-form reconstruction method for fixed-topology quintic B-spline corner smoothing is developed, yielding unified closed-form expressions for curve position and first- to third-order derivatives. Mathematical analysis proves equivalence between the proposed reconstruction and the original quintic B-spline representation. Numerical validation and efficiency evaluation demonstrate machine-precision consistency with conventional B-spline evaluation while achieving an approximately 3–7-fold speedup in curve and derivative evaluation. System-level trajectory-planning simulations further confirm reduced geometric computation load. The proposed method provides an efficient analytical evaluation framework for real-time trajectory planning and demonstrates how continuity constraints can be exploited to derive efficient analytical spline representations. Full article
(This article belongs to the Special Issue Motion Planning and Control in Autonomous Robotic Systems)
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23 pages, 4160 KB  
Article
Adaptive Adjustment of Advantage Estimation for Robot Control Using Reinforcement Learning
by Zuguo Chen, Chenghao Liang, Yi Huang, Yating Chen, Jiayu Liu, Yongwei Chen and Chaoyang Chen
Machines 2026, 14(7), 767; https://doi.org/10.3390/machines14070767 - 8 Jul 2026
Viewed by 377
Abstract
In robotics control experiments, the balance between exploration and exploitation, as well as the accuracy of the advantage function estimation, are crucial factors that affect the effectiveness of policy optimization methods. To overcome these challenges, this paper proposes an adaptive adjustment of advantage [...] Read more.
In robotics control experiments, the balance between exploration and exploitation, as well as the accuracy of the advantage function estimation, are crucial factors that affect the effectiveness of policy optimization methods. To overcome these challenges, this paper proposes an adaptive adjustment of advantage estimation based on the policy loss and policy entropy algorithm (A3E-PLE), which can improve the exploratory capabilities of the proximal policy optimization (PPO) algorithm. Specifically, on the one hand, the policy loss is adjusted using a Gaussian distribution policy entropy to mitigate randomness and separate policy improvement from random noise, thereby improving exploration efficiency. On the other hand, to adapt flexibly to various training scenarios and further enhance the accuracy of advantage function estimation, the policy loss is incorporated into the advantage function estimation. This enables the algorithm to adaptively adjust according to changes in the strategy. Finally, the proposed reinforcement learning (RL) framework was validated using robot control simulations and complex decision-making environments. It is shown that A3E-PLE achieves higher learning efficiency and greater rewards compared to traditional generalized advantage estimation. Full article
(This article belongs to the Special Issue Motion Planning and Control in Autonomous Robotic Systems)
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