Simultaneous Position and Orientation Planning of Nonholonomic Multi-Robot Systems: A Dynamic Vector Field Approach

This paper considers the simultaneous position and orientation planning of nonholonomic multi-robot systems. Different from common researches which only focus on final position constraints, we model the nonholonomic mobile robot as a rigid body and introduce both of position and orientation constraints for the robot's final states. In other words, the robot should not only reach the specified position, but also point to the desired orientation simultaneously. The challenge of this problem lies in the underactuation of full-state motion planning, since three states need to be planned by mere two control inputs. To this end, we propose a dynamic vector field (DVF) based on the rigid body modelling. Specifically, the dynamics of the robot orientation is brought into the vector field, implying that the vector field is not static on the 2D plane anymore, but a dynamic one varying with the attitude angle. Hence, each robot can move along the integral curve of the DVF to arrive at the desired position, and in the meantime, the attitude angle can converge to the specified value following the orientation dynamics. Subsequently, by designing a circular vector field under the framework of the DVF, we further study the obstacle avoidance and multi-robot collision avoidance. Finally, numerical simulation and hardware experiment are provided to verify the effectiveness.