Before revision: Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path connecting a given start and goal by transversing zero-volume constraint manifolds for a given planning problem .
After revision: Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path on the constraint manifolds between a given start and goal by transversing zero-volume constraint manifolds for a given planning problem .