Probabilistic movement primitives under unknown system dynamics

Safe Robot Trajectory Control Using Probabilistic Movement Primitives and Control Barrier Functions

In this paper, we present a novel means of control design for probabilistic movement primitives (ProMPs). Our proposed approach makes use of control barrier functions 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. 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.

Movement generalization of variable initial task state based on Euclidean transformation dynamical movement primitives

Robots need the ability to tackle problems of movement generalization in variable task state and complex environment. Dynamical movement primitives can effectively endow robots with humanoid characteristics. However, when the initial state of tasks changes, the generalized trajectories by dynamical movement primitives cannot retain shape features of demonstration, resulting in the loss of imitation quality. In this article, a modified dynamical movement primitives based on Euclidean transformation is proposed to solve this problem. It transforms the initial task state to a virtual situation similar to the demonstration and then utilizes the dynamical movement primitive method to realize movement generalization. Finally, it reverses the movement back to the real situation. Besides, the information of obstacles is added to Euclidean transformation based dynamical movement primitives framework to endow robots with the ability of obstacle avoidance. The normalized root-mean-square error is proposed as the criterion to evaluate the imitation similarity. The feasibility of this method is verified through writing letters, wiping whiteboard in two-dimensional task, and stirring mixture in three-dimensional task. The results show that the similarity of movement imitation in the proposed method is higher than dynamical movement primitives when the initial state changes. Meanwhile, Euclidean transformation based dynamical movement primitives can still greatly retain shape feature of demonstration while avoiding obstacles in an unstructured environment.