Optimal Kinodynamic Trajectory Planner for Mobile Robots in an Unknown Environment Using Bézier Contours

Trajectory planning in the field of mobile robotics involves the generation of a trajectory to navigate a robot from a start state to a goal state. One widely employed technique involves a two-step approach: a path planner generates a path made up of piecewise linear segments with sharp turns, which are then smoothed in the trajectory generation step. In contrast, this work formulates trajectory generation as an optimization problem based on the Bézier curve, denoted as ‘BTP’, to generate the robot’s trajectory in one step. It uses a weighted objective function of trajectory length and navigation time to suit different optimization strategies while considering the robot’s kinematics and dynamics limitations. BTP adopts matrix-based formulations for all mathematical operations to enable dynamic adjustment of the degree of the Bézier curve during the optimization process, if convergence is not obtained with the current degree. Additionally, BTP guarantees that the robot’s trajectory is always within the open space identified by the robot’s sensors. The efficacy of BTP has been evaluated through simulations and real-world experimentation, including soccer games and cluttered environment scenarios. Finally, the performance is benchmarked against some of the existing trajectory planners. BTP reduced the robot’s navigation time by a minimum of 11% up to 55% compared to other tested trajectory planners, ensuring $C^{2}$ continuity rather than just $C^{1}$ continuity. Furthermore, it consistently achieved precise goal configuration, unlike the tested trajectory planners, which exhibited deviations of up to 0.6 meters.