Safe Trajectory Generation for Nonholonomic Multi-Robot Systems: A Compensation-Based MPC Approach

This article investigates the collaborative trajectory generation problem for nonholonomic multi-robot systems using a compensation-based nonlinear model predictive control (MPC), where the system is subject to unknown uncertainties. A dynamic uncertainty estimator is designed for each robot to estimate the discrepancy between the predictive model and the actual system, enabling adaptive model corrections that enhance the robustness and adaptability of the MPC. By incorporating control Barrier function constraints, physical constraints, and stability constraints, the nonlinear MPC generates feasible, collision-free trajectories. These trajectories are further optimized using piecewise Bézier curves, yielding smoother and more efficient paths. Additionally, a dynamic safety-stability gain is introduced, allowing the MPC to adaptively balance safety and stability based on the system state and obstacle positions. The theoretical results are validated through simulations and experiments, demonstrating the effectiveness of the proposed approach.