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

Abstract

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. Note to Practitioners—The motivation of this article is to address the collaborative trajectory generation problem for multi-robot systems in environments with unknown uncertainties. Existing nonlinear MPC methods have two major limitations: 1) some schemes struggle to handle dynamic model uncertainties effectively, and 2) there may be adverse interactions between safety and stability components. To overcome these limitations, we propose a compensation-based nonlinear MPC framework that incorporates a dynamic uncertainty estimator for each robot. The estimator continuously measures the discrepancy between the predictive model and the actual system, adaptively updating the model to improve control accuracy. By incorporating control Barrier functions, physical, and stability constraints, the method generates feasible, collision-free trajectories. These trajectories are optimized using piecewise Bézier curves for smoother, more efficient paths. A dynamic safety-stability balancer adjusts constraints based on the system’s state and detected obstacles, relaxing stability when safety is critical and prioritizing progress when less urgent, thereby ensuring both safety and efficiency.