Local Stability Analysis and Trajectory Planning Control for Linear Motion of a Coaxial Dual-Eccentric-Mass Driven Spherical Robot
Mingwei Li, Dayong YuIntroduction/Objective:
This paper investigates the linear motion control of a coaxial dual-eccentric-mass-driven spherical robot. The objective is to resolve stability issues in the underactuated system and achieve smooth start-stop transitions through effective friction compensation.
Methods:
The kinematic model is derived under pure rolling constraints, and the dynamic model is established using the Lagrangian method. Equilibrium point analysis is performed, and local asymptotic stability is verified via Jacobian eigenvalue analysis. A quintic polynomial trajectory planning controller is proposed to regulate the swing angle of the eccentric mass. To compensate for unmodeled friction and disturbances, a cooperative control strategy combining polynomial trajectory planning with PID feedback is developed. All simulations were performed using MATLAB R2023b/Simulink.
Results:
Simulation results demonstrate that, compared with open-loop polynomial control, the proposed cooperative strategy increases steady-state velocity by 2.3% and reduces displacement deficit by 2.82 percentage points. Ground experiments confirm that the robot achieves linear motion with lateral deviation within ± 0.15 m and a displacement error of 5.84% at a target speed of 0.28 m/s.
Discussion:
The proposed method enables smooth start-stop transitions. The simulation validates that PID feedback effectively compensates for system energy loss and improves tracking accuracy. Short-distance accuracy is currently limited by stick-slip phenomena, which warrants further investigation.
Conclusion:
This study addresses the underactuated stability and smooth start-stop control challenges of a coaxial dual-eccentric-mass-driven spherical robot through a quintic polynomial trajectory planning method with PID feedback compensation. The proposed cooperative control strategy is validated through both simulation and ground experiments, providing a theoretical and practical foundation for high-precision linear motion control of spherical robots under pure rolling conditions. The results confirm that systematic trajectory planning combined with feedback compensation is an effective approach for overcoming the inherent coupling challenges in underactuated spherical robot systems.