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In traditional trajectory planning it is usually assumed that the mean path of an ensemble of open-loop trajectories is the same as would be obtained if no noise were present. However, even zero-mean noise tends to cause the mean trajectory to deviate from the nominal one. This paper introduces a stochastic model-based motion planning method to compensate for this bias. An implementation for nonholonomic mobile robots based on the kinematic cart model is provided. The examples show that the proposed method takes full advantage of the results of existing optimal trajectory planning methods, and makes the resulting mean trajectory conform to the pre-selected nominal trajectory. As a result, the average amount of online trajectory correction required of a controller is minimized.
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Abstract The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.
The field of modular self-reconfigurable robotic systems addresses the design, fabrication, motion planning, and control of autonomous kinematic machines with variable morphology. Modular self-reconfigurable systems have the promise of making significant technological advances to the field of robotics in general. Their promise of high versatility, high value, and high robustness may lead to a radical change in automation. Currently, a number of researchers have been addressing many of the challenges. While some progress has been made, it is clear that many challenges still exist. By illustrating several of the outstanding issues as grand challenges that have been collaboratively written by a large number of researchers in this field, this article has shown several of the key directions for the future of this growing field
‐arm fluoroscopy is ubiquitous in contemporary surgery, but it lacks the ability to accurately reconstruct three‐dimensional (3D) information. A major obstacle in fluoroscopic reconstruction is discerning the pose of the x‐ray image, in 3D space. Optical/magnetic trackers tend to be prohibitively expensive, intrusive and cumbersome in many applications. We present single‐image‐based fluoroscope tracking (FTRAC) with the use of an external radiographic fiducial consisting of a mathematically optimized set of ellipses, lines, and points. This is an improvement over contemporary fiducials, which use only points. The fiducial encodes six degrees of freedom in a single image by creating a unique view from any direction. A nonlinear optimizer can rapidly compute the pose of the fiducial using this image. The current embodiment has salient attributes: small dimensions ; need not be close to the anatomy of interest; and accurately segmentable. We tested the fiducial and the pose recovery method on synthetic data and also experimentally on a precisely machined mechanical phantom. Pose recovery in phantom experiments had an accuracy of in translation and 0.33° in orientation. Object reconstruction had a mean error of with STD. The method offers accuracies similar to commercial tracking systems, and appears to be sufficiently robust for intraoperative quantitative ‐arm fluoroscopy. Simulation experiments indicate that the size can be further reduced to , with only a marginal drop in accuracy.
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