In this paper, we present an innovative risk-bounded motion planning methodology for stochastic multi-agent systems. For this methodology, the disturbance, noise, and model uncertainty are considered; and a velocity obstacle method is utilized to formulate the collision-avoidance constraints in the velocity space. With the exploitation of geometric information of static obstacles and velocity obstacles, a distributed optimization problem with probabilistic chance constraints is formulated for the stochastic multi-agent system. Consequently, collision-free trajectories are generated under a prescribed collision risk bound. Due to the existence of probabilistic and disjunctive constraints, the distributed chance-constrained optimization problem is reformulated as a mixed-integer program by introducing the binary variable to improve computational efficiency. This approach thus renders it possible to execute the motion planning task in the velocity space instead of the position space, which leads to smoother collision-free trajectories for multi-agent systems and higher computational efficiency. Moreover, the risk of potential collisions is bounded with this robust motion planning methodology. To validate the effectiveness of the methodology, different scenarios for multiple agents are investigated, and the simulation results clearly show that the proposed approach can generate high-quality trajectories under a predefined collision risk bound and avoid potential collisions effectively in the velocity space.

翻译：在本文中,我们为随机多试剂系统介绍了一种创新的、有风险的多试剂系统动态规划方法;为此,考虑了扰动、噪音和模型不确定性;使用了一种速度障碍方法,以制定速度空间避免碰撞的制约因素;通过利用静态障碍和速度障碍的几何信息,为随机多试剂系统制定了具有概率概率概率限制的分散优化问题;因此,在规定的碰撞风险约束下产生了无碰撞轨迹;由于存在概率和断交的限制因素,分散的受机会限制的优化问题被重新确定为混合内位程序,采用双轨变量提高计算效率。因此,这种方法使得有可能在速度空间而不是位置空间执行运动规划任务,从而导致多试剂系统更顺畅的无碰撞轨迹和更高的计算效率;此外,潜在碰撞的风险与这种稳健的移动规划方法相捆绑在一起。为了验证该方法的有效性,对分散的受机会限制的优化优化优化优化优化优化,对多种物剂进行不同情景进行明确的模拟,并按预期地显示在高轨道上产生的风险。