RMRRT: Riemannian Barrier Metric RRT for Inequality-Aware Steering on Equality Manifolds

What happened

arXiv:2610.06863v1 Announce Type: new Abstract: This paper presents a motion planning framework that unifies equality and inequality constraints within a single geometric formulation for sampling-based planning in high-dimensional robotic systems. In conventional sampling-based planners, equality constraints are typically enforced through projection, whereas inequality constraints are handled separately through binary validity checks such as collision testing, often leading to inefficient exploration.

RMRRT first builds an ambient barrier metric from inequality-sensitive barrier terms and then induces a tangent-space metric via a (G)-orthogonal projection associated with the equality constraints. The resulting tangent-space metric is used consistently in both steering and nearest-neighbor selection, biasing exploration away from nearby inequality boundaries while preserving first-order equality consistency.