Math & Kinematics

Sampling-Based Motion Planning

Sampling-based motion planning is a family of algorithms that find collision-free paths by randomly sampling a robot's configuration space and connecting valid samples into a graph or tree, rather than discretizing the space exhaustively. Probabilistic roadmaps (PRM, Kavraki et al., 1996) and rapidly-exploring random trees (RRT, LaValle, 1998) are the canonical methods, with asymptotically optimal variants like RRT* following later. These planners scale to the high-dimensional configuration spaces of manipulator arms where grid-based search is intractable.

Why it matters for physical AI

Even as end-to-end policies advance, sampling-based planners remain the workhorse for collision-free arm motion, and hybrid systems routinely delegate free-space transit to them while policies handle contact.