Search

A complete and efficient algorithm is proposed for searching form-closure grasps of n hard fingers on the surface of a three-dimensional object represented by discrete points. Both frictional and frictionless cases are considered. This algorithm starts to search a form-closure grasp from a randomly selected grasp using an efficient local search procedure until encountering a local minimum. The local search procedure employs the powerful ray-shooting technique to search in the direction of reducing the distance between the convex hull corresponding to the grasp and the origin of the wrench space. When the distance reaches a local minimum in the local search procedure, the algorithm decomposes the problem into a few subproblems in subsets of the points according to the existence conditions of form-closure grasps. A search tree whose root represents the original problem is empolyed to perform the searching process. The subproblems are represented as children of the root node and the same procedure is recursively applied to the children. It is proved that the search tree generates O(K ln K/n) nodes in case a from-closure grasp exists, where K is the number of the local minimum points of the distance in the grasp space and n is the number of fingers. Compared to the exhaustive search, this algorithm is more efficient, and, compared to other heuristic algorithms, the proposed algorithm is complete in the discrete domain. The efficiency of this algorithm is demonstrated by numerical examples. Index Terms--Discrete domain, fixture layout design, form closure, grasp synthesis, multifingered robotic hand.

For a class of robot arms, a proportional derivative (PD) controller plus gravity compensation yields the global asymptotic stability for regulation tasks, and some proportional-integral-derivative (PID) controllers guarantee local regulation without gravity cancellation. However, these controllers cannot render asymptotic stability for tracking tasks. In this paper, a simple decentralized continuous sliding PID controller for tracking tasks that yields semiglobal stability of all closed-loop signals with exponential convergence of tracking errors is proposed. A dynamic sliding mode without reaching phase is enforced, and terminal attractors, as well as saturated ones, are considered. A comparative experimental study versus PD control, PID control, and adaptive control for a rigid robot arm validates our design. Index Terms--Proportional-integral-derivative (PID) control, robot manipulators, sliding mode control, terminal attractors.

Delay-dependent/delay-independent uniform asymptotic stability and uniform stability criteria for linear systems with multiple time-varying delays are established respectively in this note. The results are derived based on a new-type stability theorem for retarded dynamical systems and a new analysis technique for estimating the derivative of a Lyapunov function along the solution of a system at certain specific instants. Four remarks together with an illustrative example are given to compare the obtained results with and to show their superiority to those in the literature. Index Terms--Linear systems, Lyapunov methods, stability, time delay.

Fixtures play an important role in many manufacturing operations such as inspection, machining, and part fabrication. In the development of a fixture, it is desired that the feasible fixturing surfaces and optimal fixturing points on the workpiece be selected automatically. In this paper, an algorithm is presented to automate the generation of optimal fixturing points, which totally restrains the workpiece in the fixture, i.e., satisfies the form-closure condition, as well as minimizes the workpiece positional errors. First, a heuristics is proposed for searching a set of fixturing surfaces capable of providing form-closure. Then, we formulate the problem of determining optimal fixturing points on the eligible set of fixturing surfaces as a quadratic programming problem with the workpiece positioning accuracy as the performance index and the robust form-closure requirement as the linear constraints. Finally, the implementation for three numerical examples demonstrates the usefulness and efficiency of the proposed algorithm. Index Terms--Fixture design, form-closure, grasping, precise localization.

Two distributed cooperation controllers are presented for trajectory tracking of two manipulators which are cooperatively handling an object. The controllers control the positions of the robots distributively by using the trajectory error of the object in the task space. In the first controller, the internal force between the object and a manipulator is controlled only by a feedforward of the desired force. The second controller uses a force feedback. No communication is required between the manipulators in both the controllers. Their globally and exponentially asymptotic stabilities are guaranteed by Lyapunov functions.

An algorithm for finding the shortest path of a disc among a set of polygonal obstacles is presented. Let [N.sub.t] denote the total number of obstacle vertices and [N.sub.c] the number of convex vertices. Our algorithm uses a radius-independent data structure called extended tangent graph (ETG) which registers collision-free tangents of the obstacles according to different discs and takes [Mathematical Expression Omitted] space. The ETG depends only on original obstacles, and it is constructed in advance without using any information about the disc in O(([N.sub.c] + k)[N.sub.t]) computation time, where k is the number of outer common tangents of the obstacles. It takes O([N.sub.t] log [N.sub.t]) time to partially update the ETG to reflect the start and goal of a given disc. The shortest path is planned by a graph-search algorithm.

The tangent graph is a powerful graphic data structure for the path-planning of a mobile robot among obstacles because it has fewer edges than the widely used visibility graph. This paper proposes an efficient algorithm for computing the tangent graph of a set of polygonal obstacles. The algorithm at first detects common tangents of obstacle boundaries by moving-line processing that cooperatively moves a straight segment on the boundaries, and then checks for intersections among detected tangents and the obstacles both by a sequential approach and a sweep-line technique. It is proved that the moving-line processing takes O(MN) and O([M + R]N) computation time in the best and worst cases, respectively, where N expresses the number of obstacle vertices, and M denotes the number of convex segment chains of the obstacle boundaries, and R is a parameter representing the complexity of the boundaries.