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We propose a new approach to deform robot trajectories based on affine transformations. At the heart of our approach is the concept of affine invariance: Trajectories are deformed in order to avoid unexpected obstacles or to achieve new objectives but, at the same time, certain definite features of the original motions are preserved. Such features include, for instance, trajectory smoothness, periodicity,...
This paper discusses an online dynamic motion generation scheme for nonprehensile object manipulation by using a set of predefined motions and a trajectory deformation algorithm capable of incorporating positional and velocity boundary constraints. By creating optimal trajectories offline and deforming them online, computational complexity during execution is reduced considerably. As tight convex...
Humanoids locomote by making and breaking contacts with their environment. Thus, a crucial question for them is to anticipate whether a contact will hold or break under effort. For rigid surface contacts, existing methods usually consider several point-contact forces, which has some drawbacks due to the underlying redundancy. We derive a criterion, the Contact Wrench Cone (CWC), which is equivalent...
This paper presents an incremental sampling-based approach for trajectory imitation in cluttered environments using the RRT* algorithm. Inspired by the discrete Laplace-Beltrami operator the underlying distance metric is based upon the difference from a reference trajectory through a quadratic distance term incorporating velocity and acceleration deviations along the trajectory. Mathematically-backed...
The panorama of probabilistic completeness results for kinodynamic planners is still confusing. Most existing completeness proofs require strong assumptions that are difficult, if not impossible, to verify in practice. To make completeness results more useful, it is thus sensible to establish a classification of the various types of constraints and planning methods, and then attack each class with...
Planning collision-free, dynamically-balanced movements for humanoid robots is a challenging problem. An effective approach consists of first planning a motion satisfying geometric and kinematic constraints (such as collision avoidance, joint angle limits, velocity limits, etc.) and, in a second stage, modifying this motion so that it respects dynamic balance criteria, such as those relative to the...
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