Probabilistic Collision Avoidance For Multiple Robots: A Closed Form PDF Approach

This paper proposes a novel method for reactive multiagent collision avoidance by characterizing the longitudinal and lateral intent uncertainty along a trajectory as a closed-form probability density function. Intent uncertainty is considered as the set of reachable velocities in a planning interval and distributed as a Gaussian distribution over the robot's instantaneous velocity. We utilize the Time Scaled Collision Cone(TSCC) approach, which characterizes the space of instantaneous collision avoidance velocities available to the egoagent. We introduce intent uncertainty into the characteristic equation of the TSCC to derive the closed-form probability density function, which allows the collision avoidance problem to be rewritten as a deterministic optimization procedure. The formulation also allows the flexibility for the inclusion of confidence intervals for collision avoidance. We thus demonstrate the results and ablation studies of this derived collision avoidance formulation on various confidence intervals.