Diffeomorphic Transforms for Generalised Imitation Learning

We address the generalised imitation learning problem of producing robot motions to imitate expert demonstrations, while adapting to novel environments. Past studies have often focused on methods that closely mimic demonstrations. However, to operate reliably in novel environments, robots should be able to adapt their learned motions accordingly. Motivated by this, we devise a framework capable of learning a time-invariant dynamical system to imitate demonstrations, and generalise to account for changes to the surroundings. To ensure the system is robust to perturbations, we need to maintain its stability. Our framework enforces stability in a principled manner: we start with a known stable system and use differentiable bijections (diffeomorphisms) to morph the system into the desired target system. We modularise robot motion and develop diffeomorphic transforms to encode individual actions. A composition of transforms produces generalised behaviour that complies with multiple requirements, such as mimicking demonstrations while avoiding obstacles. We evaluate our framework in both simulation and on a real-world 6-DOF JACO manipulator. Results show our framework is capable of producing a stable system that is collision-free and incorporates user-specified biases, while closely resembling demonstrations.