A novel approach to dynamic movement imitation based on quadratic programming

This paper proposes a novel approach to generate trajectories that generalize given demonstrations according to optimality criteria. By formulating the problem as a quadratic program we can efficiently incorporate constraints to adapt to new desired motion requirements while achieving the main goal of matching the acceleration profile of the demonstration. This makes our method particularly suited for the imitation and generalization of trajectories such as hitting movements, where it is crucial to maintain the dynamic traits of the demonstration while respecting strict requirements for the goals position, velocity and time. Our method draws inspiration from the Dynamical Movement Primitives (DMPs) framework, preserving its desirable properties of flexibility and rejection of disturbances during execution. Moreover, it offers an higher degree of control on the generated solution, allowing for example i) to limit the instantaneous positions, velocities and accelerations during the whole trajectory, and ii) to add intermediate way points that were not present in the demonstration. With current state-of-the-art solvers of quadratic programs, a problem with hundreds of parameters can be solved in tens of milliseconds in a standard computer, allowing practical applications. Our methodology results in trajectories with a very good approximation of the shape traits of the demonstration, with additional flexibility in specifying constraints of the generated trajectory.