Generalizing demonstrated motions and adaptive motion generation using an invariant rigid body trajectory representation

Abstract

In programming by demonstration, generalization is necessary to apply demonstrated motions in novel situations. Many existing trajectory representations have poor generalization capabilities since they are built on trajectory coordinates that depend on the context in which the motion is recorded. In order to generalize, the user is typically required to perform a large number of varied demonstrations. This paper instead emphasizes the usefulness of an invariant trajectory representation to separate essential motion information from context-specific information of the recorded demonstrations. The invariants are interpreted as the control inputs of a dynamical system describing the evolution of the trajectory. New trajectories are generated for novel situations as the solution of a constrained optimal control problem in which context-specific information of the novel situation is encoded in the constraints. Results indicate how, starting from only a single demonstration, new trajectories can be generated in novel situations while maintaining similarity with the original demonstration. Invariance in trajectory representations therefore proves useful to reduce the number of necessary demonstrations to learn and apply new motions.