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

cs.ROFeb 17, 2026

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

Authors: Branimir Ćaran, Vladimir Milić, Marko Švaco, Bojan Jerbić

Organizations: Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia · Croatian Academy of Sciences and Arts, Zagreb 10000, Croatia

Abstract

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.

Figures & tables

Panel of Figure 1 — Fig. 1: Mobile robot schematics.

Panel of Figure 2 — Fig. 2: Block diagram of the overall control system for the considered mobile robot.

Fig. 3: Experimental setup of the mobile robot on a vertical surface (left) and a horizontal surface (right).

Parameter	Description	Value
$r$	Wheel radius	$0.0254~\mathrm{m}$
$a$	Half-length of robot body	$0.1125~\mathrm{m}$
$b$	Half-width of robot body	$0.1125~\mathrm{m}$
$m$	Robot mass	$3.50~\mathrm{kg}$
$m_{w}$	Wheel mass	$0.03203~\mathrm{kg}$
$I_{\theta}$	Robot yaw inertia	$0.03333~\mathrm{kgm^{2}}$

TABLE I: Robot physical parameters.

Experiment i) – Lissajous trajectory on horizontal surface
Controller	RMSE	No Dist.	Norm. Dist.	Norm.-Ax. Dist.
Lyap. PI + FF	$e_{x}$	0.008	0.009	0.010
	$e_{y}$	0.010	0.011	0.012
	$e_{\theta}$	0.082	0.085	0.086
	$\mathrm{TV}_{v}$	7.76	8.45	15.54
	$\mathrm{TV}_{f}$	16.64	15.09	16.14

TABLE II: Tracking performance across the three experiments.

Fig. 4: Experimental responses of the robot without disturbance, compared across the three different controllers. Green arrows indicate robot orientation.

Fig. 5: Experimental responses of the robot subjected to a normal disturbance, compared across the three different controllers. Green arrows indicate robot orientation.

Fig. 6: Experimental responses of the robot subjected to a normal and axial disturbance, compared across the three different controllers. Green arrows indicate robot orientation.

Fig. 7: Trajectory tracking with proposed Lyap. PI + FF on horizontal plane. Green arrows indicate robot orientation.

Fig. 8: Trajectory tracking with proposed Lyap. PI + FF on vertical surface. Green arrows indicate robot orientation.

PID Control

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1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
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Department of Mechanical & Industrial Engineering at the New Jersey Institute of Technology, Newark, NJ 07102, USA · School of Engineering and Sustainable Development at the De Montfort University, Leicester, LE1 9BH, UK

May 26, 2026J/K move · Enter open · S save

L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking

Quan Quan, Hao Li

1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Robotic Control Robot Trajectory Tracking Lyapunov-Based Control Data-Driven Control

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This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.

Abstract

PID Control

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