Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing

Nowadays, autonomously operated nonholonomic vehicles are employed in a wide range of applications, ranging from relatively simple household chores (e.g. carpet vacuuming and lawn mowing) to highly sophisticated assignments (e.g. outer space exploration and combat missions). Each application may require different levels of accuracy and capabilities from the vehicles, yet, all expect the same critical outcome: to safely complete the task while avoiding collisions with obstacles and the environment. Herein, we report on a bounded control law for nonholonomic systems of unicycle-type that satisfactorily drive a vehicle along a desired trajectory while guaranteeing a minimum safe distance from another vehicle or obstacle at all times. The control law is comprised of two parts. The first is a trajectory tracking and set-point stabilization control law that accounts for the vehicle's kinematic and dynamic constraints (i.e. restrictions on velocity and acceleration). We show that the bounded tracking control law enforces global asymptotic convergence to the desired trajectory and local exponential stability of the full state vector in the case of set-point stabilization. The second part is a real-time avoidance control law that guarantees collision-free transit for the vehicle in noncooperative and cooperative scenarios independently of bounded uncertainties and errors in the obstacles' detection process. The avoidance control acts locally, meaning that it is only active when an obstacle is close and null when the obstacle is safely away. Moreover, the avoidance control is designed according to the vehicle's acceleration limits to compensate for lags in the vehicle's reaction time. The performance of the synthesized control law is then evaluated and validated via simulation and experimental tests.