In this article, a recently developed approach for robot motion planning is extended and applied to non-holonomic mobile robots. This approach replace random sampling by deterministic one. We present several implementations of PRM-based planners: 1) Classical PRM with deterministic sampling and random sampling, 2) Deterministic and random Lazy-PRM, and 3) Lattice-based PRM. We have used several low-discrepancy sequences (Halton, Hammersley, Faure, and Sobol) and low-discrepancy lattices. Experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original PRM.

This work deals with the sensor-based motion planning problem for car-like robots. Sensor-based versions of Lazy DRM and Lazy LRM are used to exploit the information obtained from sensors and to compute a feasible collision-free path. The algorithm tries to reach the goal, executing the local method in the known free region. If it succeeds, a path to the goal is found and the algorithm finishes. Otherwise, the algorithm executes more scans to extend its free space, an so on. We have performed some simulations that show the promise of our approach.