We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to traverse in order to solve the task. We specify a class of sequential motion planning problems that fulfill a particular property of the change in the free configuration space when transitioning between manifolds. For this problem class, we develop the algorithm Planning on Sequenced Manifolds (PSM*) which searches for optimal intersection points between manifolds by using RRT* in an inner loop with a novel steering strategy. We provide a theoretical analysis regarding PSM*s probabilistic completeness and asymptotic optimality. Further, we evaluate its planning performance on multi-robot object transportation tasks.
