From Multi-Modal Paths to Executable Trajectories: A Trajectory Planning Framework for 4WIS Robots

Runjiao Bao; Lin Zhang; Yongkang Xu; Shoukun Wang

cs.ROAug 29, 2026

From Multi-Modal Paths to Executable Trajectories: A Trajectory Planning Framework for 4WIS Robots

Authors: Runjiao Bao, Lin Zhang, Yongkang Xu, Shoukun Wang

Organizations: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China · School of Automation, Beijing Institute of Technology, Beijing 100081, China · Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518000, China

Abstract

Four-wheel independent steering (4WIS) mobile robots support multiple motion modes, offering high maneuverability in narrow and complex environments. However, existing planning methods often fail to fully exploit these capabilities, leading to suboptimal trajectory quality. To address this limitation, this paper proposes a multi-modal global trajectory planning framework that couples mode-augmented front-end search with mode-consistent segment-wise trajectory optimization. In the front-end stage, Hybrid A* is extended to a four-dimensional state space incorporating motion modes, while mode-switching-aware cost and heuristic functions embed mode decisions into the global search process. Multi-modal Reeds-Shepp curves and an intelligent terminal connection strategy are further designed to improve search efficiency. In the back-end stage, a segment-wise trajectory optimization framework based on an improved iterative safe corridor scheme is developed to convert discrete multi-modal paths into smooth, kinematically feasible trajectories with stationary mode transitions. Experimental results show that the proposed method achieves the best overall performance in safety, arrival time, terminal accuracy and computation time. Real-world experiments on a physical 4WIS robot further validate the practical effectiveness and executability of the generated trajectories, providing a flexible and high-performance solution for multi-modal mobile robot trajectory planning.

Figures & tables

Fig. 1: Configuration of the 4WIS robot.

Fig. 2: The overall architecture diagram of the 4WIS multi-modal global trajectory planning framework.

Fig. 3: Multi-modal motion sampling. (a) Ackermann steering. (b) Lateral steering. (c) Parallel movement.

Fig. 4: Improved adaptive safe corridor construction process. (a) Obstacle dilatation. (b) Direction decision. (c) Rapid expansion. (d) Detailed expansion.

Parameter	Value	Parameter	Value
1. Robot Physical and Kinematic Parameters
Length ( $l$ )	1.00 m	Width ( $w$ )	0.62 m
Wheelbase ( $L$ )	0.68 m	Track width ( $W$ )	0.52 m
Max steering angle ( $\phi_{\text{max}}$ )	$30^{\circ}$	Max steering rate ( $\dot{\phi}_{\text{max}}$ )	$180^{\circ}$ /s
Mode switch time ( $t_{\text{switch}}$ )	0.4 s	Max acceleration ( $a_{\text{max}}$ )	5.0 m/s 2
Reference velocity ( $v_{\text{ref}}$ )	1.0 m/s	Max velocity ( $v_{\text{max}}$ )	1.0 m/s

TABLE I: Key Parameters of the 4WIS Robot and Trajectory Planner

Fig. 5: Visualization of planned trajectories across the four benchmark scenarios.

Scenario	Method	Experimental Metrics
Scenario	Method	SF	TL (m)	AT (s)	AC (m -1 )	MC (m -1 )	TPE (m)	TYE (rad)	SMR	CT (ms)
Env1	ICR	✗	43.623	55.008	0.256	1.511	0.000	0.000	0.728	31293
	MPPI	✓	43.587	58.550	0.202	2.082	0.095	0.087	0.904	26097
	Single-SC	✓	48.396	49.592	0.186	1.695	0.000	0.000	1.000	9074.1
	Multi-SC	✓	45.790	46.387	0.193	1.695	0.000	0.000	1.000	5526.0
Env2	ICR	✗	15.146	19.759	0.310	1.616	0.000	0.000	0.715	2881.8

TABLE II: Performance comparison of trajectory planning methods across benchmark scenarios.

Fig. 6: Ablation visualization in representative scenario.

Method	Experimental Metrics
Method	SF	TL (m)	TPE (m)	TYE (rad)	CT (ms)
Only MP	✓	18.700	0.202	0.003	116.8
MP+RS	✓	18.745	0.000	0.000	185.0
MP+SCH	✓	15.500	0.195	0.003	131.8
Full	✓	15.235	0.000	0.000	35.44

TABLE III: Ablation comparison in representative scenario.

Fig. 7: Effect of reference velocity on motion mode switching behavior.

Fig. 8: Real-world experiment results. (a) Experimental environment and navigation process. (b) Comparison between the single-modal and multi-modal trajectories. (c) Lateral and longitudinal tracking errors during execution.

Robot Motion Planning

Robot motion planning finds safe, feasible paths and trajectories for robots moving through constrained, changing environments.

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Lyapunov-Based PI-Like Control for Robust Trajectory Tracking of a Four-Wheel Independently Driven and Steered Robot: Design and Experimental Validation

Branimir Ćaran, Vladimir Milić, Marko Švaco, Bojan Jerbić

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PID Control Robot Trajectory Tracking Feedback Control Mobile Robotics Robust Control Lyapunov-Based Control

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In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.

Abstract

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