Differentiable Motion Manifold Primitives for Reactive Motion Generation under Kinodynamic Constraints

Abstract

Real-time motion generation -- which is essential for achieving reactive and adaptive behavior -- under kinodynamic constraints for high-dimensional systems is a crucial yet challenging problem. We address this with a two-step approach: offline learning of a lower-dimensional trajectory manifold of task-relevant, constraint-satisfying trajectories, followed by rapid online search within this manifold. Extending the discrete-time Motion Manifold Primitives (MMP) framework, we propose Differentiable Motion Manifold Primitives (DMMP), a novel neural network architecture that encodes and generates continuous-time, differentiable trajectories, trained using data collected offline through trajectory optimizations, with a strategy that ensures constraint satisfaction -- absent in existing methods. Experiments on dynamic throwing with a 7-DoF robot arm demonstrate that DMMP outperforms prior methods in planning speed, task success, and constraint satisfaction.