**Learning Equality Constraints for Motion Planning on Manifolds**
Giovanni Sutanto (USC); Isabel Rayas Fernández (University of Southern California)*; Peter Englert (University of Southern California); Ragesh Kumar Ramachandran (University of Southern California); Gaurav Sukhatme (University of Southern California)
Constrained robot motion planning is a widely used technique to solve complex robot tasks. We consider the problem of learning representations of constraints from demonstrations with a deep neural network, which we call Equality Constraint Manifold Neural Network (ECoMaNN). The key idea is to learn a level-set function of the constraint suitable for integration into a constrained sampling-based motion planner. Learning proceeds by aligning subspaces in the network with subspaces of the data. We combine both learned constraints and analytically described constraints into the planner and use a projection-based strategy to find valid points. We evaluate ECoMaNN on its representation capabilities of constraint manifolds, the impact of its individual loss terms, and the motions produced when incorporated into a planner.