Adaptive MPC and nonlinear tracking control for non-holonomic robots in cluttered spaces

This paper presents the implementation of trajectory planning and control for a non-holonomic robotic platform. Non-holonomic systems introduce significant challenges in motion planning and control due to their kinematic constraints. The proposed approach integrates graph-based path planning with trajectory optimization and employs both nonlinear control and model predictive control (MPC) for accurate trajectory tracking. The kinematic model of a unicycle-type robot is utilized, and two path planners Probabilistic Roadmaps (PRM) and Hybrid A* are evaluated, with Hybrid A* selected for its ability to generate kinematically feasible paths. Trajectory optimization is formulated as a nonlinear optimal control problem, solved using direct single-shooting and multiple-shooting methods, with the latter proving more robust. A quadratic cost function penalizes state and input deviations while enforcing obstacle avoidance through geometric constraints. For trajectory tracking, a nonlinear feedback controller and an MPC-based approach are implemented and compared. Simulation results demonstrate that the nonlinear controller achieves precise tracking, while MPC exhibits robustness with slight oscillations in heading angle regulation. The study concludes that combining optimization-based trajectory planning with advanced control strategies ensures stable and efficient navigation for non-holonomic robots in constrained environments.