Journal of Mechanisms and Robotics-Transactions of the Asme最新文献

This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.

This paper studies the problem of computing an average (or mean) displacement from a set of given spatial displacements using three types of parametric representations: Euler angles and translation vectors, unit quaternions and translation vectors, and dual quaternions. It is shown that the use of Euclidean norm in the space of unit quaternions reduces the problem to that of computing the mean for each quaternion component separately and independently. While the resulting algorithm is simple, a change in the sign of a unit quaternion could lead to an incorrect result. A novel kinematic measure based on dual quaternions is introduced to capture the separation between two spatial displacements. This kinematic measure is used to define the variance of a set of displacements, which is then used to formulate a constrained least squares minimization problem. It is shown that the problem decomposes into that of finding the optimal translation vector and the optimal unit quaternion. The former is simply the centroid of the set of translation vectors and the latter is obtained as the eigenvector corresponding to the least eigenvalue of a 4 × 4 positive definite symmetric matrix. In addition, it is found that the weight factor used in combining rotations and translations in the formulation does not play a role in the final outcome. Examples are provided to show the comparisons of these methods.

This work tackles practical issues which arise when using a tendon-driven robotic manipulator (TDRM) with a long, flexible, passive proximal section in medical applications. Tendon-driven devices are preferred in medicine for their improved outcomes via minimally invasive procedures, but TDRMs come with unique challenges such as sterilization and reuse, simultaneous control of tendons, hysteresis in the tendon-sheath mechanism, and unmodeled effects of the proximal section shape. A separable TDRM which overcomes difficulties in actuation and sterilization is introduced, in which the body containing the electronics is reusable and the remainder is disposable. An open-loop redundant controller which resolves the redundancy in the kinematics is developed. Simple linear hysteresis compensation and re-tension compensation based on the physical properties of the device are proposed. The controller and compensation methods are evaluated on a testbed for a straight proximal section, a curved proximal section at various static angles, and a proximal section which dynamically changes angles; and overall, distal tip error was reduced.