Path planning, obstacle avoidance, and trajectory control of a differential-drive mobile robot based on improved RRT∗-APF and nonsingular quasi-sliding mode techniques.

This study presents a framework for path planning, trajectory generation, and trajectory control of a differential-drive mobile robot in obstacle-populated environments. In the path-planning phase, an improved RRT∗-APF (rapidly-exploring random tree star and artificial potential field) method is developed by integrating RRT∗ with APF, safety inflation, and a steering-aware smoothness cost. Furthermore, parent-node selection and connection in RRT∗ are determined by a indicator designed to consider path length, obstacle risk, and smoothness. The generated path is optimized by greedy pruning and cubic B-spline smoothing to obtain a trackable geometric route. In addition, a phase-plane time-optimal method is used to transform the smoothed path into a feasible time-indexed trajectory under velocity and acceleration constraints. In the trajectory-control phase, a tracking module based on nonsingular quasi-sliding mode control (NSQSMC) is implemented as a practical component to execute the generated time-indexed trajectory on the physical robot platform. The simulation and experimental results verify the effectiveness of the proposed framework. Compared with the structurally closest RRT∗-APF baseline, the proposed planner reduces composite path cost by 5.9% and 2.9% and obstacle-risk cost by 32.5% and 12.6% in the mixed-obstacle and maze scenarios, respectively. These improvements remain statistically significant after Holm correction. The greedy-pruning-B-spline pipeline further improves trajectory smoothness by reducing accumulated heading variation by 22.22% and 17.34% in the two scenarios while maintaining sufficient obstacle clearance. Moreover, compared with the conventional sliding mode controller (SMC), the NSQSMC-based tracking implementation reduces the planar position-error IAE, MAE, and RMSE by 73.2%, 72.3%, and 67.3%, respectively. Compared with the backstepping controller (BC), the corresponding reductions are 56.2%, 55.2%, and 46.7%, respectively.