Safe Robot Trajectory Control Using Probabilistic Movement Primitives and Control Barrier Functions - Davoodi, Mohammadreza; Iqbal, Asif; Cloud, Joseph M.; Beksi, William J.; Gans, Nicholas R. (Frontiers in Robotics and AI, 2022)
In this paper, we present a novel means of control design for probabilistic movement primitives (ProMPs). ProMPs are a powerful tool for defining a distribution of robot trajectories. However, existing control methods to execute desired motions suffer from a number of drawbacks. For example, these methods tend to rely on linear control designs thus limiting their applicability in robotics. In addition, they tend to be overly sensitive to initial parameters which can lead to stability issues. Conversely, our proposed approach makes use of control barrier and control Lyapunov functions defined by a ProMP distribution. Thus, a robot may move along a trajectory within the distribution while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. The control employs feedback linearization to handle nonlinearities in the system dynamics and real-time quadratic programming to ensure a solution exists that satisfies all safety constraints while minimizing control effort. We extend this approach to include time-varying CBFs which can be incorporated to avoid static and moving obstacles. Furthermore, we highlight how the proposed method may allow a designer to emphasize certain safety objectives that are more important than the others. A series of simulations and experiments demonstrate the efficacy of our approach and show it can run in real time.