Motion can be described in several alternative representations, including joint configuration or end-effector spaces, but also more complex topology-based representations that imply a change of Voronoi bias, metric or topology of the motion space. Certain types of robot interaction problems, e.g. wrapping around an object, can suitably be described by so-called writhe and interaction mesh representations. However, considering motion synthesis solely in a topology-based space is insufficient since it does not account for additional tasks and constraints in other representations. In this paper, we propose methods to combine and exploit different representations for synthesis and generalization of motion in dynamic environments. Our motion synthesis approach is formulated in the framework of optimal control as an approximate inference problem. This allows for consistent combination of multiple representations (e.g. across task, end-effector and joint space). Motion generalization to novel situations and kinematics is similarly performed by projecting motion from topology-based to joint configuration space. We demonstrate the benefit of our methods on problems where direct path finding in joint configuration space is extremely hard whereas local optimal control exploiting a representation with different topology can efficiently find optimal trajectories. In real-world demonstrations, we highlight the benefits of using topology-based representations for online motion generalization in dynamic environments.

This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem is not tractable for state-ofthe-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator.

Many practical tasks in robotic systems, such as cleaning windows, writing, or grasping, are inherently constrained. Learning policies subject to constraints is a challenging problem. In this paper, we propose a method of constraint-aware learning that solves the policy learning problem using redundant robots that execute a policy that is acting in the null space of a constraint. In particular, we are interested in generalizing learned null-space policies across constraints that were not known during the training. We split the combined problem of learning constraints and policies into two: first estimating the constraint, and then estimating a null-space policy using the remaining degrees of freedom. For a linear parametrization, we provide a closed-form solution of the problem. We also define a metric for comparing the similarity of estimated constraints, which is useful to pre-process the trajectories recorded in the demonstrations. We have validated our method by learning a wiping task from human demonstration on flat surfaces and reproducing it on an unknown curved surface using a force-or torque-based controller to achieve tool alignment. We show that, despite the differences between the training and validation scenarios, we learn a policy that still provides the desired wiping motion.

Abstract-A large class of motions can be decomposed into a movement task and null-space policy subject to a set of constraints. When learning such motions from demonstrations, we aim to achieve generalisation across different unseen constraints and to increase the robustness to noise while keeping the computational cost low. There exists a variety of methods for learning the movement policy and the constraints. The effectiveness of these techniques has been demonstrated in lowdimensional scenarios and simple motions. In this paper, we present a fast and accurate approach to learning constraints from observations. This novel formulation of the problem allows the constraint learning method to be coupled with the policy learning method to improve policy learning accuracy, which enables us to learn more complex motions. We demonstrate our approach by learning a complex surface wiping policy in a 7-DOF robotic arm.

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