Adria Colome and Carme Torras
Movement Primitives (MPs) have been widely used over the last years for learning robot motion tasks with direct Policy Search (PS) reinforcement learning. Among them, Probabilistic Movement Primitives (ProMPs) are a kind of MP based on a stochastic representation over sets of trajectories, which benefits from the properties of probability operations. However, the generation of such ProMPs requires a set of demonstrations to capture motion variability. Additionally, using context variables to modify trajectories coded as MPs is a popular approach nowadays in order to adapt motion to environmental variables. This paper proposes a contextual representation of ProMPs that allows for an easy adaptation to changing situations through context variables, by reparametrizing motion with them. Moreover, we propose a way of initializing contextual trajectories without the need of real robot demonstrations, by setting an initial position, a final position, and a number of trajectory interest points, where the contextual variables are evaluated. The parametrizations obtained show to be accurate while relieving the user from the need of performing costly computations such as conditioning. Additionally, using this contextual representation, we propose a simple yet effective quadratic optimization-based obstacle avoidance method for ProMPs. Experiments in simulation and on a real robot show the promise of the approach.
We initialized a 2-dimensional trajectory on the x-y domain with a fixed initial point and variable end point, and used the proposed approach to fit a contextual model. We then conditioned the trajectory end point to be 10cm away from the mean end point. Moreover, we placed two obstacles successively and implemented our approach to avoid them, giving the most importance to the Y component, as seen in the video.
Fig. 1: Contextual model: Conditioning and avoiding obstacles.