Topology-based representations for motion planning and generalization in dynamic environments with interactions

Abstract

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.

Reinforcement Learning in Topology-based Representation for Human Body Movement with Whole Arm Manipulation

“…For our two motion generation scenarios, we combine Writhe matrix and Laplacian coordinates to represent the robot-humanoid relationship, similar to [19,24]. To this end, we abstract the bodies of the robot and the humanoid into a set of curves consisting of line segments, as seen in Fig.…”

Space-time area coverage control for robot motion synthesis

“…In our previous work [11], we have shown the effects of choosing an alternate space for motion planning. It is often possible to exploit a task representation, such as the one we propose in this paper, which renders a complex motion in the joint space as a simple, linear motion in the alternate space.…”

“…Methods for optimising robot motion with respect to a cost function have been proposed, ranging from sampling based approaches [16] to optimal control [13]. In our previous work [11], we discuss how the task spaces y can be constructed in a way that improves the convergence of local optimisation methods. In other terms, we construct spaces where successful trajectories are easier to find (in case of sampling methods), shorter or local (in case of optimisation methods) in an appropriate space, thus avoiding the need for more expensive global planning methods.…”

HDRM: A Resolution Complete Dynamic Roadmap for Real-Time Motion Planning in Complex Scenes

“…Generally, motion planning can be categorized into optimizationbased and sampling-based algorithms. Optimization-based methods [1], [2] generate optimal trajectories with respect to cost functions, but may get stuck in local minima and fail to produce a valid solution when the problem is non-convex or ill-defined. On the other hand, sampling-based approaches [3], [4], [5], [6] promise to solve complex problems by sampling globally in the configuration space.…”