Tejas Parekh1 Arun Kumar Singh1 K. Madhava Krishna1
In this paper, we address the problem of reactive collision avoidance among multiple robots. However we impose the constraint of continuous curvature on the collision avoidance manoeuvre which adds to the complexity of the problem but is necessary for realistic implementation of collision avoidance among multiple non-holonomic robots like tricycles and car-like. Since these non-holonomic robots cannot execute point-turn motion, performing collision avoidance with these robots while maintaining curvature continuity becomes a very challenging problem. Hence the proposed work comes as an enhancement over the existing reactive collision avoidance frameworks which completely neglect the above aspects. We modify the collision cone approach of collision avoidance to the case of multiple robots moving with nonlinearly varying velocities. This is done by approximating the vehicle evolution with a smooth function represented as a linear combination of orthogonal basis functions and writing the collision avoidance condition as analytical function with respect to time. As a direct consequence of that, the reactive collision avoidance and goal-reaching could be solved as a constrained optimization problem. The theory is substantiated by extensive simulations for various bench-mark cases.