Probabilistic Movement Primitive Control via Control Barrier Functions

In this paper, we introduce a novel means of control design for probabilistic movement primitives (ProMPs). ProMPs are a powerful tool to define a distribution of trajectories for robots or other dynamic systems. However, existing control methods to execute desired motions suffer from a number of drawbacks such as a reliance on linear control approaches and sensitivity to initial parameters. We propose the use of feedback linearization, quadratic programming, and multiple control barrier functions to guide a system along a trajectory within the distribution defined by a ProMP, while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. This allows for better performance on nonlinear systems and offers firm stability and known bounds on the system state. Furthermore, we highlight how the proposed method may allow a designer to emphasize certain objectives that are more important than the others. A series of simulations demonstrate the efficacy of our approach and show it can run in real time.