Real-time swept volume and distance computation for self collision detection

Abstract

We present a real-time self collision detection algorithm applicable for industrial and humanoid robots. The algorithm is based on computing the swept volumes of all bodies and checking them pairwise for collisions. The algorithm operates on joint angle intervals. Such, it does not only test a single or N intermediate configurations but assures safety of a whole movement. Key idea of the new swept volume computation is representing volumes as convex hulls extended by a buffer radius, so called sphere swept convex hulls (SSCH). This leads to tight and compact bounding volumes. The operation set available to model the different joints is strictly conservative and allows for a trade-off between accuracy and computation time. During a configurable timespan the algorithm updates a table of pairwise distances and thus can guarantee hard realtime. It is applied on DLR's humanoid Justin in a sports robotic scenario, where also accuracy and computational performance is evaluated (0.4ms, INTEL T2500@2GHz).

Overapproximative arm occupancy prediction for human-robot co-existence built from archetypal movements

“…There exists no previous work that can rigorously predict the set of future occupancies given an uncertain dynamic model of human motion. The mapping of uncertain joint angles to the occupancy of a kinematic chain has been considered in [28] in an overapproximative way. A nonformal approach to compute the set of future occupancies is described in [29], which considers the future occupancy of the human given some maximum joint velocities, where these velocities are assumed.…”

“…2(g). To the best of our knowledge, there exists only one approach that computes overapproximative occupancies of kinematic chains efficiently, which is that of Täubig et al [28]. Here, the occupancy of each link on a kinematic chain is represented as a sphere-swept volume (SSV), defined as the Minkowski sum of a convex hull of points with a zero-centered sphere.…”

“…The set of points of the SSV is generated sequentially from a given initial SSV enclosing the i th link in its own (i th) coordinate system. For each joint down to the base of the kinematic chain, the algorithm from [28] sequentially generates a new SSV, which encloses the link in the i − 1th coordinate system under all positions of the i th joint. This SSV in its turn is then used to generate a new SSV enclosing the link in the i − 2th coordinate system under all positions of the i − 1th joint, and so on until the (fixed) base coordinate system.…”

“…Hence, the SSV enclosing the end effector has at least m • 2 p 3 r points, where m points define the end-effector occupancy in its own coordinate system, and the kinematic chain has p prismatic and r rotational joints. We refer the reader to [28] for a detailed description of the algorithm.…”

“…The algorithm from [28] creates an SSV defined by a set of points, which is generated sequentially from an initial set as described in Section V-E. At each DOF, the set of points is multiplied by two (prismatic DOF) or at least three (rotational DOF) different transformation matrices to generate a new set of cardinality twice or thrice the previous set. Since the transformation matrices are constant size, the number of multiplication operations is proportional to the number of points in the new set obtained.…”