Null-Space-Based Time-Varying Formation Control of Uncertain Nonlinear Second-Order Multi-Agent Systems with Collision Avoidance

In this paper, the time-varying formation control problem with collision avoidance is addressed for uncertain nonlinear second-order multi-agent systems in a null-space-based behavioral control architecture. To guarantee the tracking and coordination performance simultaneously, a novel and flexible time-varying formation task strategy is designed where only neighborhood information is necessary. Moreover, the agent radius and a sine function are introduced such that the collision avoidance task function describes collision risk more accurately in contrast to existing results. Then, two fixed-time sliding mode controllers with constant and variable exponent coefficients, respectively, are proposed to track the desired trajectory generated by null space projection. Also, the theoretical results for the task design and trajectory tracking are obtained by using the Lyapunov stability theory. Numerical simulation and practical experiments are finally conducted to illustrate the effectiveness and superiority of the proposed method.