Hybrid Safety Certificate for Fast Collision Checking in Sampling-Based Motion Planning

Safety certificates in robot configuration space have been shown as an efficient collision checking method. However, this method can only be applied to very simple problems since constructing the configuration space obstacles is often intractable. In this paper we propose a hybrid safety certificate (HSC) approach in both the configuration space and the workspace to increase collision checking efficiency for large-scale complex motion planning problems. Specifically, the collision-free certificate regions are constructed as random spheres in the configuration space. While the in collision certificate regions are constructed using the inside spheres of the workspace obstacles. In fact, the HSC method realizes collision checking as a straightforward sphere-sphere overlapping test which is widely regarded as the simplest way for collision detection. Besides the lazy collision checking strategy can be naturally combined with our high efficient HSC method. The HSC method combining with the lazy planning strategy is applied to both the feasible and the optimal motion planning problems. And we present a feasible motion planner BiHSC and an optimal motion planner BiHSC*. Simulations demonstrate that the computation speed is much faster than that of the state-of-the-art algorithms.