Learning Robotic Cutting from Demonstration: Non-Holonomic DMPs using the Udwadia-Kalaba Method

Dynamic Movement Primitives (DMPs) offer great versatility for encoding, generating and adapting complex end-effector trajectories. DMPs are also very well suited to learning manipulation skills from human demonstration. However, the reactive nature of DMPs restricts their applicability for tool use and object manipulation tasks involving non-holonomic constraints, such as scalpel cutting or catheter steering. In this work, we extend the Cartesian space DMP formulation by adding a coupling term that enforces a pre-defined set of non-holonomic constraints. We obtain the closed-form expression for the constraint forcing term using the Udwadia-Kalaba method. This approach offers a clean and practical solution for guaranteed constraint satisfaction at run-time. Further, the proposed analytical form of the constraint forcing term enables efficient trajectory optimization subject to constraints. We demonstrate the usefulness of this approach by showing how we can learn robotic cutting skills from human demonstration.