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.

Abstract-Motion can be described in alternative representations, including joint configuration or end-effector spaces, but also more complex topological 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 topological spaces is insufficient since it does not cater for additional tasks and constraints in other representations. In this paper we propose methods to combine and exploit different representations for motion synthesis, with specific emphasis on generalization of motion to novel situations. Our approach is formulated in the framework of optimal control as an approximate inference problem, which allows for a direct extension of the graphical model to incorporate multiple representations. Motion generalization is similarly performed by projecting motion from topological to joint configuration space. We demonstrate the benefits 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. Further, we illustrate the successful online motion generalization to dynamic environments on challenging, real world problems.

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Abstract-This paper proposes a novel approach for the synthesis of grasps of objects whose geometry can be observed only in the presence of noise. We focus in particular on the problem of generating caging grasps with a realistic robot hand simulation and show that our method can generate such grasps even on complex objects. We introduce the idea of using geodesic balls on the object's surface in order to approximate the maximal contact surface between a robotic hand and an object. We define two types of heuristics which extract information from approximate geodesic balls in order to identify areas on an object that can likely be used to generate a caging grasp. Our heuristics are based on two scoring functions. The first uses winding angles measuring how much a geodesic ball on the surface winds around a dominant axis, while the second explores using the total discrete Gaussian curvature of a geodesic ball to rank potential caging postures. We evaluate our approach with respect to variations in hand kinematics, for a selection of complex real-world objects and with respect to its robustness to noise.

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