Collision Avoidance of Arbitrarily Shaped Deforming Objects Using Collision Cones

Abstract

In this letter, the problem of collision avoidance of objects, which can deform by changing their shape as a function of time, is considered. There are several scenarios involving such deforming objects-examples include environments with shape shifting robots, such as snake robots, boundaries of swarms of vehicles, and boundaries of oil spills. There is very limited work in the literature that considers dynamic environments comprising such shape changing entities. To develop conditions that predict the onset of collision for deformable objects, this letter uses the notion of collision cones in environments involving engagements between a point object and a deforming object, a circular object and a deforming object, and finally, an arbitrarily shaped object and a deforming object. The collision cone equations are subsequently embedded in a Lyapunov framework and used to develop nonlinear analytical guidance laws for collision avoidance in such environments. Simulations are performed to demonstrate the efficacy of the guidance laws.