It is promising but challenging to design flocking control for a robot swarm to autonomously follow changing patterns or shapes in a optimal distributed manner. The optimal flocking control with dynamic pattern formation is, therefore, investigated in this paper. A predictive flocking control algorithm is proposed based on a Gibbs random field (GRF), where bio-inspired potential energies are used to charaterize "robot-robot" and "robot-environment" interactions. Specialized performance-related energies, e.g., motion smoothness, are introduced in the proposed design to improve the flocking behaviors. The optimal control is obtained by maximizing a posterior distribution of a GRF. A region-based shape control is accomplished for pattern formation in light of a mean shift technique. The proposed algorithm is evaluated via the comparison with two state-of-the-art flocking control methods in an environment with obstacles. Both numerical simulations and real-world experiments are conducted to demonstrate the efficiency of the proposed design.

Motion planning is challenging for multiple robots in cluttered environments without communication, especially in view of real-time efficiency, motion safety, distributed computation, and trajectory optimality, etc. In this paper, a reinforced potential field method is developed for distributed multi-robot motion planning, which is a synthesized design of reinforcement learning and artificial potential fields. An observation embedding with a self-attention mechanism is presented to model the robot-robot and robot-environment interactions. A soft wall-following rule is developed to improve the trajectory smoothness. Our method belongs to reactive planning, but environment properties are implicitly encoded. The total amount of robots in our method can be scaled up to any number. The performance improvement over a vanilla APF and RL method has been demonstrated via numerical simulations. Experiments are also performed using quadrotors to further illustrate the competence of our method.