Dual Null-Space Based Controller Design with Signal Compensation for Formation with Conflicted Tasks

Abstract

In this paper, we consider the multi-agent formation problem with trajectory tracking and obstacle avoidance. Out of all the controllers proposed to solve the multi-task problem, null-space based controller stood out for its ability of task priority appointment, priority interchangeability, and the simplicity in Lyapunov stability analysis. However, the advantages above are mainly based on the assumption that the considered tasks are mutually non-conflicted, which is not always the case. We propose a null-space based controller that takes the lower-rank task's control signal as the higher-rank controller's input, and redesign higher-rank controller so that the eliminated control signal is partially compensated and the tasks' aggregated error is decreased. We also design a dual null-space controller in order to apply virtual leader for path planning, which enables obstacle avoidance and tracking while the target tracking point is in an inadmissible condition. We verify the performance of formation and tracking control with and without dynamic obstacles, and show the decrease in aggregated error compared with the traditional null-space controller.