Showing papers on "Motion planning published in 1983"

Formulation and optimization of cubic polynomial joint trajectories for industrial robots

Abstract: Because of physical constraints, the optimum control of industrial robots is a difficult problem. An alternative approach is to divide the problem into two parts: optimum path planning for off-line processing followed by on-line path tracking. The path tracking can be achieved by adopting the existing approach. The path planning is done at the joint level. Cubic spline functions are used for constructing joint trajectories for industrial robots. The motion of the robot is specified by a sequence of Cartesian knots, i.e., positions and orientations of the hand. For an N -joint robot, these Cartesian knots are transformed into N sets of joint displacements, with one set for each joint. Piecewise cubic polynomials are used to fit the sequence of joint displacements for each of the N joints. Because of the use of the cubic spline function idea, there are only n - 2 equations to be solved for each joint, where n is the number of selected knots. The problem is proved to be uniquely solvable. An algorithm is developed to schedule the time intervals between each pair of adjacent knots such that the total traveling time is minimized subject to the physical constraints on joint velocities, accelerations, and jerks. Fortran programs have been written to implement: 1) the procedure for constructing the cubic polynomial joint trajectories; and 2) the algorithm for minimizing the traveling time. Results are illustrated by means of a numerical example.

Retraction: A new approach to motion-planning

Abstract: The two-dimensional Movers' Problem may be stated as follows: Given a set of polygonal obstacles in the plane, and a two-dimensional robot system B, determine whether one can move B from a given placement to another without touching any obstacle, and plan such a motion when one exists. Efficient algorithms are presented for the two special cases in which B is either a disc or a straightline segment, running respectively in time 0(n log n) and 0(n2 log n). To solve the problem for a disc one uses the planar Voronoi diagram determined by the obstacles; in the case of a line-segment one generalizes the notion of Voronoi diagram to the 3-dimensional configuration space of the moving segment.

Hypothesizing Channels through Free-Space in Solving the Findpath Problem

Abstract: : Channels are an encoding of free-space corresponding to the classes of paths within an environment. An implementation exploiting this global model of the connectivity of free-space has been able to solve 2-dimensional find-path problems in several minutes which formerly took many hours. The author's algorithm is essentially a problem-solving strategy using a homeomorphic reduction of the search space. Given a polyhedral environment, a technique is presented for hypothesizing a channel volume through the free space containing a class of successful collision-free paths. A set of geometric constructions between obstacle faces is proposed, and defined is a mapping from a field of view analysis to a direct local construction of free space. The algorithm has the control structure of a search which propagates construction of a connected channel towards a goal along a frontier of exterior free faces. Thus a channel volume starts out by surrounding the moving object in the initial configuration and grows towards the goal. Finally, techniques for analyzing the channel decomposition of free space and suggesting a path are shown. This paper addresses issues in the find-path or piano mover's problem in robotics and spatial planning: the problem involves finding a path for a solid object in an environment containing obstacles. In robotics we are typically interested in motion planning for a mobile robot or manipulator. In Computer-Aided Design, the problem of automated structural design for n structural members is also an instance of the most general form of the mover's problem.

Suboptimal control of industrial manipulators with a weighted minimum time-fuel criterion

Abstract: Even if a manipulator does not have to follow a prespecified path (i.e. a geometric path and a velocity schedule), due to the complexity and nonlinearity of the manipulator dynamics, control of manipulators has been conventionally divided into two sub-problems, namely path planning and path tracking, which are then separately and independently solved. This may result in mathematically tractable solutions but can not offer a solution that utilizes manipulators' maximum capabilities (e.g. operating them at their maximum speed). To combat this problem, we have developed a suboptimal method for controlling manipulators that provides improved performance in both their operating speed and use of energy. The nonlinearity and the joint couplings in the manipulator dynamics-- a major hurdle in the design of robot control--are handled by a new concept of averaging the dynamics at each sampling interval. With the averaged dynamics, we have derived a feedback controller which (i) has a simple structure allowing for on-line implementation with inexpensive microprocessors, and (ii) offers a near minimum time-fuel(NMTF) solution, thus enabling manipulators to perform nearly up to their maximum capacity and efficiency. As a demonstrative example, we have applied the method to control the Unimation PUMA 600 series manipulator and simulated its performance on a DEC VAX-11/780. The simulation results agree with the expected high performance nature of the control method.

Industrial robot that moves around unexpected obstacles with a minimum distance

Abstract: Maneuvering an industrial robot to avoid a collision with obstacles in real time involves not only the fast obstacle detection and description, but also fast decision making. The problem is complicated since no a-priori knowledge about obstacles is assumed. In addition, they may appear in the robot's path unexpectedly. In this paper, the detection and description are achieved by the use of stereo cameras. Through the top view of the workspace, the cameras furnish the silhouette as well as heights of obstacles. To speed up the image processing, pixel array is grouped into patches and the maximum height of each patch is determined. To simplify the obstacle description in the computer, "pillar" model of the bounding polyhedra is constructed. Fast decision making is accomplished by structuring a finite number of possible collision avoidance paths. Path feasibility is determined at the "module aisle" level while optimization is performed at the subpath level so that the order of the problem is reduced from 63 to 3 × 6.