Velocity-Free Consensus and Obstacle Avoidance in a Non-rectangular Bounded Space

In this paper, we consider the cooperative control of second-order agents in a non-rectangular bounded space. Note that the previous consensus design based on velocity projection along rectangular bouncing boundaries cannot be directly applied in non-rectangular space, a mirrored matrix is introduced to convert the rebound particle velocity into the continuous mirrored velocity and then the non-rectangular bounded space can be expanded into an infinite space. Considering that the agent's velocity cannot be measured accurately or is difficult to measure, a velocity-free consensus algorithm is proposed to accomplish the flocking in a non-rectangular bounded space based on the state observer. For the purposed of applying the proposed consensus algorithm into the real robots, an obstacle avoidance algorithm based on potential function is added into the consensus algorithms. The effectiveness of the analytical results is verified by numerical simulations.