Motion Planning of 3D Nonholonomic Robots via Curvature-Constrained Vector Fields

Vector-field-based methods are typical feedback planning algorithms, especially eligible for the motion planning of nonholonomic robots. Nevertheless, most existing vector fields (VF) do not account for the prevalent constraints on robot’s kinematics. This paper addresses the motion planning problem for 3D nonholonomic robots with trajectories featuring upper bounded curvature. To this end, a curvature-constrained VF over $\mathbb{R}^{3}$ is proposed, whose integral curves guarantee an upperbound of curvature as well as an almost-global attraction region towards the desired position with a specified heading direction. Moreover, a control strategy is presented to determine the robot’s control inputs subject to the curvature constraint. Under the designed control laws, the robot is guaranteed to track the VF while ensuring that the actual trajectory adheres to the curvature constraint. Finally, the efficacy of the presented motion planning algorithm is validated by numerical simulations.