Integrated Analysis of Mapping, Path Planning, and Advanced Motion Control for Autonomous Robotic Navigation
Abstract
1. Introduction
2. Environment Representation Using Occupancy-Based Mapping
2.1. Binary Occupancy Maps
2.2. Probabilistic Occupancy Maps
3. Sampling-Driven Path Planning Algorithms
3.1. Probabilistic Roadmap (PRM)
3.2. A* and Hybrid A* Algorithms
3.3. Rapidly Exploring Random Tree (RRT)
4. Advanced Motion Control Techniques
4.1. PID and Fractional-Order PID Controllers (FOPIDs)
4.2. State Feedback Controller (SFC)
4.3. Model Predictive Controller (MPC)
5. Results and Discussions
5.1. Performance Analysis of Path Planning Algorithms
5.1.1. Case 1: Manually Defined Map
5.1.2. Case 2: Map Created from Image
5.1.3. Case 3: Map Created from LiDAR Scans and Poses
5.1.4. Case 4: Randomly Generated Map
5.2. Performance Analysis of Motion Control Techniques
- —longitudinal position of the vehicle [m];
- —longitudinal velocity of the vehicle [m/s];
- —longitudinal acceleration of the vehicle [m/s2];
- m—mass of the vehicle [kg];
- —net tractive/braking force applied at the wheels [N];
- —air density [kg/m3];
- —aerodynamic drag coefficient;
- A—frontal cross-sectional area of the vehicle [m2];
- g—gravitational acceleration ( m/s2);
- —road slope angle [rad];
- —rolling resistance coefficient;
- —measured output, taken as the vehicle longitudinal velocity [m/s].
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ARA* | Anytime Repairing A* |
BiRRT | Bidirectional Rapidly Exploring Random Tree |
BIT | Batch Informed Trees |
FOPID | Fractional-order PID |
IAE | Integral of Absolute Error |
LiDAR | Light Detection and Ranging |
MAE | Mean Absolute Error |
MPC | Model Predictive Control |
PID | Proportional-Integral-Derivative |
PRM | Probabilistic Roadmaps |
RMSE | Root Mean Square Error |
ROS | Robot Operating System |
RRT | Rapidly Exploring Random Tree |
RTAB | Real-Time Appearance-Based Mapping |
SFC | State Feedback Control |
SLAM | Simultaneous Localisation and Mapping |
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Aspect | Description |
---|---|
Structure | Grid (2D or 3D) of discrete cells. |
Cell Values | 0: free space; 1: occupied (obstacle); : probability of occupancy. |
Binary Occupancy Map | Each cell is either free (0) or occupied (1). |
Probabilistic Occupancy Map | Each cell stores a probability value for occupancy. |
3D Occupancy Map (Octomap) | Extends to 3D using voxel-based representation. |
Technique/Metrics | Case 1 | Case 2 | Case 3 | Case 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
PL | CT | SM | PL | CT | SM | PL | CT | SM | PL | CT | SM | |
PRM | 136.89 | 0.082 | 0.75 | 738.37 | 64.731 | 3.50 | 38.39 | 0.721 | 0.18 | 480.72 | 64.40 | 0.20 |
A* with Euclidean | 129.30 | 0.008 | 1.26 | 735.46 | 0.131 | 0.51 | 39.59 | 0.143 | 1.03 | 421.00 | 0.142 | 0.00 |
A* with Chebyshev | 129.30 | 0.008 | 1.24 | 737.22 | 0.125 | 0.51 | 39.59 | 0.165 | 1.02 | 422.29 | 0.139 | 0.00 |
A* with Euclidean Squared | 166.08 | 0.006 | 1.52 | 860.98 | 0.061 | 0.51 | 40.58 | 0.112 | 1.06 | 463.73 | 0.101 | 0.00 |
A* with Manhattan | 129.30 | 0.007 | 1.26 | 756.17 | 0.114 | 0.51 | 39.83 | 0.115 | 1.06 | 429.90 | 0.144 | 0.00 |
Hybrid A* | 131.86 | 0.325 | 1.29 | 726.05 | 22.58 | 3.28 | 40.29 | 20.766 | 1.59 | 700.82 | 136.39 | 0.18 |
RRT | 169.82 | 3.227 | 1.07 | 973.55 | 7.198 | 3.73 | 55.36 | 0.054 | 3.11 | – | – | – |
RRT* | 170.07 | 3.150 | 1.54 | 953.04 | 6.589 | 4.06 | 43.10 | 0.065 | 1.27 | – | – | – |
BiRRT | 160.12 | 5.008 | 1.58 | 922.11 | 5.884 | 3.97 | 49.05 | 0.031 | 1.53 | – | – | – |
Controller | Sinusoidal Path Without Disturbances | Sinusoidal Path with Dynamic Disturbances | ||||
---|---|---|---|---|---|---|
MAE | RMSE | IAE | MAE | RMSE | IAE | |
PID | 1.40 | 2.26 | 140.19 | 1.98 | 2.89 | 198.03 |
FOPID | 1.19 | 1.68 | 119.65 | 1.21 | 1.69 | 121.72 |
SFC | 0.37 | 0.64 | 37.01 | 0.38 | 0.80 | 38.81 |
MPC | 0.09 | 0.59 | 9.89 | 0.19 | 0.65 | 19.46 |
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Bingi, K.; Singh, A.P.; Ibrahim, R.; Rajamallaiah, A.; Shaik, N.B. Integrated Analysis of Mapping, Path Planning, and Advanced Motion Control for Autonomous Robotic Navigation. Fractal Fract. 2025, 9, 640. https://doi.org/10.3390/fractalfract9100640
Bingi K, Singh AP, Ibrahim R, Rajamallaiah A, Shaik NB. Integrated Analysis of Mapping, Path Planning, and Advanced Motion Control for Autonomous Robotic Navigation. Fractal and Fractional. 2025; 9(10):640. https://doi.org/10.3390/fractalfract9100640
Chicago/Turabian StyleBingi, Kishore, Abhaya Pal Singh, Rosdiazli Ibrahim, Anugula Rajamallaiah, and Nagoor Basha Shaik. 2025. "Integrated Analysis of Mapping, Path Planning, and Advanced Motion Control for Autonomous Robotic Navigation" Fractal and Fractional 9, no. 10: 640. https://doi.org/10.3390/fractalfract9100640
APA StyleBingi, K., Singh, A. P., Ibrahim, R., Rajamallaiah, A., & Shaik, N. B. (2025). Integrated Analysis of Mapping, Path Planning, and Advanced Motion Control for Autonomous Robotic Navigation. Fractal and Fractional, 9(10), 640. https://doi.org/10.3390/fractalfract9100640