Generating Continuous Paths On Learned Constraint Manifolds Using Policy Search

Many robotic manipulation tasks are constrained due to kinematic limitations placed on the object being manipulated. This increases the complexity of manipulation tasks that operate in high dimensions, leading to increased risk that sampling based planners are unable to find optimal solutions. Whilst trajectory optimisation methods provide guaranteed optimal solutions when implementing constraints, they only provide locally optimal solutions in sequential decision-making and struggle to provide globally optimal paths. These constraints can be incorporated into the probabilistic latent spaces by using demonstrations that satisfy the constraint function. However whenever constraints change or a manipulator must perform different tasks the network must be retrained to accommodate the new constraints. In this paper, we provide an approach that allows the training of a single learned manifold that can be augmented to determine the constraint manifold for the manipulation task. Using this manifold, the geodesic between two points can be computed using policy search to solve the cost function associated with the geodesic curve length ${\mathcal{L}_\gamma }$. We provide comparisons in terms of path length against popular path planning algorithms with different kinematic constraints, demonstrating our method’s ability to find optimal shortest paths on constraint manifolds.