  Placing robots outside controlled conditions requires versatile movement
representations that allow robots to learn new tasks and adapt them to
environmental changes. The introduction of obstacles or the placement of
additional robots in the workspace, the modification of the joint range due to
faults or range-of-motion constraints are typical cases where the adaptation
capabilities play a key role for safely performing the robot's task.
Probabilistic movement primitives (ProMPs) have been proposed for representing
adaptable movement skills, which are modelled as Gaussian distributions over
trajectories. These are analytically tractable and can be learned from a small
number of demonstrations. However, both the original ProMP formulation and the
subsequent approaches only provide solutions to specific movement adaptation
problems, e.g., obstacle avoidance, and a generic, unifying, probabilistic
approach to adaptation is missing. In this paper we develop a generic
probabilistic framework for adapting ProMPs. We unify previous adaptation
techniques, for example, various types of obstacle avoidance, via-points,
mutual avoidance, in one single framework and combine them to solve complex
robotic problems. Additionally, we derive novel adaptation techniques such as
temporally unbound via-points and mutual avoidance. We formulate adaptation as
a constrained optimisation problem where we minimise the Kullback-Leibler
divergence between the adapted distribution and the distribution of the
original primitive while we constrain the probability mass associated with
undesired trajectories to be low. We demonstrate our approach on several
adaptation problems on simulated planar robot arms and 7-DOF Franka-Emika
robots in a dual robot arm setting.
