Showing papers on "Motion planning published in 1986"

On multiple moving objects

Abstract: This paper explores the motion planning problem for multiple moving objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration space-time that represents the time-varying constraints imposed on the moving object by the other moving and stationary objects. The planner represents this space-time approximately, using two-dimensional slices. The space-time is then searched for a collision-free path. The paper demonstrates this approach in two domains. One domain consists of translating planar objects; the other domain consists of two-link planar articulated arms.

A concept for manipulator trajectory planning

Abstract: Following a prescribed trajectory with a manipulator tip in an ideal manner results in a one DOF overall motion whatever the configuration of the manipulator and of the path might be. Thus, a transformation of the equations of motion from joint coordinates to path coordinates leads to a set, which cannot only be solved by formal quadrature but defines as well the phase space of admissible motion constrained by path geometry and joint torques. Time optimal solution representing the maximum mobility of the path-manipulator-configuration can be determined by a field of extremals bounded by a maximum velocity curve, which acts as a trajectory source or sink. Its properties lead to an algorithm for evaluating the time-minimum-curve from a sequence of accelerating/decelerating extremals. Additional optimizing criteria are regarded applying Bellman's principle.

Multiresolution path planning for mobile robots

Abstract: The problem of automatic collision-free path planning is central to mobile robot applications. An approach to automatic path planning based on a quadtree representation is presented. Hierarchical path-searching methods are introduced, which make use of this multiresolution representation, to speed up the path planning process considerably. The applicability of this approach to mobile robot path planning is discussed.

Dynamic path planning for a mobile automaton with limited information on the environment

Abstract: The problem of path planning is studied for the case of a mobile robot moving in an environment filled with obstacles whose shape and positions are not known. Under the accepted model, the automaton knows its own and the target coordinates, and has a "sensory" feedback which provides it with local information on its immediate surroundings. Ibis information is shown to be sufficient to guarantee reaching a global objective (the target), while generating reasonable (if not optimal) paths. A lower bound on the length of paths generated by any algorithm operating with uncertainty is formulated, and two nonheuristic path planning algorithms are described. In the algorithms, motion planning is done continuously (dynamically), based on the automaton's current position and on its feedback. The effect of additional sources of information (e.g., from a vision sensor) on the outlined approach is discussed.

Collision Detection for Moving Polyhedra

Abstract: We consider the collision-detection problem for a three-dimensional solid object moving among polyhedral obstacles. The configuration space for this problem is six-dimensional, and the traditional representation of the space uses three translational parameters and three angles (typically Euler angles). The constraints between the object and obstacles then involve trigonometric functions. We show that a quaternion representation of rotation yields constraints which are purely algebraic in a seven-dimensional space. By simple manipulation, the constraints may be projected down into a six-dimensional space with no increase in complexity. The algebraic form of the constraints greatly simplifies computation of collision points, and allows us to derive an efficient exact intersection test for an object which is translating and rotating among obstacles.

Integrated path planning and dynamic steering control for autonomous vehicles

Abstract: A method is presented for combining two previously proposed algorithms for path-planning and dynamic steering control into a computationally feasible scheme for real-time feedback control of autonomous vehicles in uncertain environments. In the proposed approach to vehicle guidance and control, Path Relaxation is used to compute critical points along a globally desirable path using a priori information and sensor data. Generalized potential fields are then used for local feedback control to drive the vehicle along a collision-free path using the critical points as subgoals. Simulation results are presented to demonstrate the control scheme.

Using backprojections for fine motion planning with uncertainty

Abstract: This paper outlines a method for planning motions in the presence of uncertainty. Tasks are modeled as geometrical goals in configuration space. The planning process consists of determining regions from which particular motions are guar anteed to reach a desired goal successfully. An algorithm is presented for backprojecting from desired goal states. The backprojection regions are computed by erecting constraints that geometrically capture the uncertainty in motion. The relationship of backprojections to goal recognizability is discussed within the formal framework of preimages. This relationship suggests a partitioning of desired goal states into recognizable goal states. Backprojections are actually per formed from this partitioning.

Determining the minimum translational distance between two convex polyhedra

Abstract: Given two objects we define the minimal translational distance (MTD) between them to be the length of the shortest relative translation that results in the objects being in contact. MTD is equivalent to the distance between two objects if the objects are not intersecting; however MTD is also defined for intersecting objects and it then gives a measure of penetration. We show that the computation of MTD can be recast as a configuration space problem, and describe an algorithm for computing MTD for convex polyhedra. This research was conducted under the McDonnell Douglas Independent Research and Development Program.

Fast, three-dimensional, collision-free motion planning

Abstract: Issues dealing with fast, 3-D, collision-free motion planning are discussed, and a fast path planning system under development at NBS is described. The components of a general motion planner are outlined, and some of their computational aspects are discussed. It is argued that an octree representation of the obstacles in the world leads to fast path planning algorithms. The system we are developing uses such an octree representation. The robot and its swept-volume paths are approximated by primitive shapes so as to result in fast collision detection algorithms. The search for a path is performed in the octree space, and combines hypothesize and test, hill climbing, and A.

An algorithmic approach to the automated design of parts orienters

Abstract: This paper concerns the design of parts orienters - the dual to the motion planning problem. Two particular paradigms are considered and their abstractions to the computational domain lead to interesting problems in graph pebbling and function composition on finite sets. Polynomial time algorithms are developed for the abstracted problems.

A strategy for obstacle avoidance and its application to mullti-robot systems

Abstract: We present a local method for obstacle avoidance based on the existence of extreme separating hyperplanes. Its application is then extended to the coordinated motion of several mobile robots, and to the avoidance of two manipulators. The techniques of local planning we develop here prove to be an interesting substitute to the potential field method, as they provide a simple geometric support for the analysis.

Time optimal trajectory planning for robotic manipulators with obstacle avoidance: A CAD approach

Abstract: A method is presented which finds the minimum time motions for a manipulator between given end states. The method considers the full nonlinear manipulator dynamics, actuator saturation characteristics, and accounts for both the presence of obstacles in the work space and restrictions on the motions of the manipulator's joints. The method is computationally practical and has been implemented in a Computer Aided Design (CAD) software package, OPTARM II, which facilitates its use. Examples of its application to a six degree-of-freedom articulated manipulator, performing tasks in a typical environment, are presented. The results show that substantial improvements in system performance can be achieved with the technique.

A collision detection algorithm based on velocity and distance bounds

Abstract: The collision detection problem is encountered whenever objects are to be manipulated in the real world. Efficient solutions to this problem must intelligently decide when in time and where in space to check for interference among the objects. Complete solutions must guarantee that no collision can be overlooked. Useful solutions should also report the precise space/time points at which colliding objects begin and end contact. An algorithm based on velocity and distance bounds is described which is both useful and complete. Experiments are presented which measure the efficiency of the algorithm on a variety of test cases. The algorithm is contrasted with existing collision detection methods.

Motion of Objects in Contact

Abstract: The use of computers in the design, manufacture, and ma nipulation of physical objects is increasing. An important aspect of reasoning about such actions concerns the motion of objects in contact. The study of problems of this nature requires not only the ability to represent physical objects but also the development of a framework or theory in which to reason about them. In this paper such a development is in vestigated and a fundamental theorem concerning the motion of objects in contact is proved. The simplest form of this theorem states that if two objects in contact can be moved to another configuration in which they are in contact, then there is a way to move them from the first configuration to the second configuration such that the objects remain in contact throughout the motion. This result is proved when translation and rotation of objects are allowed. The problem of more generalized types of motion is also discussed. This study has obvious applications in compliant motion and in motion planning.

Coordinated motion of two robot arms

Abstract: We study the problem of planning simultaneous motion for two robot arms that are modeled on the Stanford arm. The arms have two degrees of freedom and must move in a workspace, avoiding obstacles and each other. We develop an O(n2logn) algorithm for planning motion of two arms with tips together, and an O(n3) algorithm for independent but synchronized motion. Here n is the total number of walls of the obstacles.

Robot motion planning with uncertainty in the geometric models of the robot and environment: A formal framework for error detection and recovery

Abstract: This paper addresses robot motion planning with uncertainty in sensing, control, and the geometric models of the robot and environment. To this end, a formal framework for error detection and recovery is proposed.

Minimum-time navigation of an unmanned mobile robot in a 2-1/2D world with obstacles

Abstract: In a 2-1/D world an isolines-based world representation is employed. An algorithm of navigation is proposed based upon polygonization of the isolines, and use of the vertices of the polygon as nodes in the graph search. Quanitative recommendations are given concerning the required density of isolines and the error of polygonization. When a physical model of mechanical motion is applied, this algorithm of navigation provides minimum-time trajectories of motion. The results of navigation are illustrated using a simulation system developed for an Intelligent Mobile Autonomous System (unmanned robot).

Automatic grasp planning in the presence of uncertainty

Abstract: This paper presents a method for automatic planning of robot grasping motions that are insensitive to bounded uncertainties in the object's location. The method exploits the physics of friction to generate all grasp plans that utilize either a squeez-grasp, offset-grasp, or push-grasp motion. All plans that are found will succeed even if the worst-case error occurs. From this space of plans, a plan can be chosen and executed without sensing or feedback. Moreover, executing the motion removes two degrees of uncertainty from the object's position. For simplicity, planar motion of the object during grasping is assumed. The planner has been implemented, and the resulting program has been tested on an industrial manipulator.

Minimum-time trajectory planning for industrial robots with general torque constraints

Abstract: There are a number of trajectory planning algorithms which generate the joint torques/forces required to drive a robot along a given geometric path in minimum or near-minimum time [1, 3, 5, 6, 7, 9]. These methods make fairly specific assumptions about the form of the joint torque/force constraints, thereby limiting their applicability. A method, called the perturbation trajectory improvement algorithm (PTIA), is developed here which can generate the joint positions, velocities, and torques required to move a robot along a specified geometric path in minimum time under very general torque constraints. The PTIA starts with a non-optimal trajectory which meets all the required torque constraints, and perturbs the trajectory in such a way as to always decrease the traversal time for the path. This perturbation process continues until the torque constraints prevent any further improvement in the traversal time. The torque constraints may be expressed in terms of quantities related to torque rather than torque itself; it is possible, for example, to limit velocity, acceleration, jerk, and motor voltage, either singly or in combination. The perturbation trajectory planner also is very simple to implement, and many of the calculations are independent of each other and can therefore be done in parallel, As a demonstrative example, the PTIA is applied to the first three joints of the Bendix PACS Arm.

Pathfinding in multi-robot systems: Solution and applications

Abstract: In the paper a general approach is given to the solution of the findpath problem in multi-robot systems based on a suitable structuring of the hierarchical overall system. The method developed uses a systematic design procedure for multi-robot systems which includes the design of the hierarchical coordinator for on-line collision avoidance. The efficiency of this new approach is demonstrated by several cases like the interaction of three stationary robots with different obstacles as well as by the interaction of mobile robots and moving obstacles.

Continuous motion planning in unknown environment for a 3D cartesian robot arm

Abstract: The approach (called Continuous Path Planning, or CPP) developed in [1,10] for non-heuristic path planning for a point automaton or various planar robot arms moving in an environment with unknown obstacles, is extended here on a three-dimensional (3D) cartesian arm. The task is to move the arm endpoint from the starting to a target position. The arm body is assumed to be capable of "feeling" a contact (physical or at a distance) with an obstacle. With such local information, the convergence to a global goal can be assured. No constraints are imposed on the shape of the obstacles.

A hierarchical orthogonal space approach to three-dimensional path planning

Abstract: A methodology for three-dimensional collision-free path planning by which planning is done in the three-dimensional orthogonal two-dimensional projections of a three-dimensional environment is presented, Collision checking is done in each of the three orthogonal two-dimensional subspaces using primitive path segments. A hierarchical-path search method is used to speed up the search process. This approach forms basis for spatial planning in environments where no a priori knowledge is assumed. The three orthogonal two-dimensional projections can be readily obtained from three orthogonal cameras in simple environments.

Reducing multiple object motion planning to graph searching

Abstract: In this paper we study the motion planning problem for multiple objects where an object is a 2-dimensional body whose faces are line segments parallel to the axes of $R^{2}$ and translations are the only motions allowed. Towards this end we analyze the structure of configuration space, the space of points that correspond to positions of the objects. In particular, we consider CONNECTED, the set of all points in configuration space that correspond to configurations of the objects where the objects form one connected component. We show that CONNECTED consists of faces of various dimensions such that if there is a path in CONNECTED between two 0-dimensional faces (vertices) of CONNECTED then there is a path between them along 1-dimensional faces (edges) of CONNECTED. It is known that if there is a motion between the configurations. Thus by the result of this paper the existence of a motion between two vertices of CONNECTED implies a motion corresponding to a path along edges of CONNECTED. Hence we have reduced the motion planning problem from a search of a high dimensional space to a graph searching problem. Searching the graph of vertices and edges of CONNECTED for a path has a prohibitive worse-case complexity because of the large number of vertices and edges. However, if the search generates edges and vertices only as they are needed, a practical and efficient algorithm may be possible using some effective heuristic. From this result it is shown that motion planning for rectangles in a rectangular boundary is in PSPACE. Since it is known that the problem is PSPACE-hard we conclude it is a PSPACE-complete problem.

Minimum time path planning for a robot

Abstract: A new algorithm of minimum time motion planning is proposed for robots operating in the obstacle strewn environment. Structure of the topological passageways is analyzed and represented using a model of slalom situations for which a number of rules is determined. Dynamical system of robot is described in a form of sequential machine. This enabled a merger between two kindred algorithms: A* search algorithm, and dynamic programming. An experimental analysis of the simulated mobile robot has confirmed the applicability of results.

An intelligent system for an autonomous vehicle

Abstract: This paper describes an intelligent full-size autonomous vehicle system which simultaneously performs multiple constraint path planning from a DMA data base and goal properties list, obstacle avoidance, and road following. Path planning and obstacle avoidance were successfully demonstrated in March 1985; road following will be demonstrated in February 1986. These results are made possible by the coupling of several procedural and knowledge-based subsystems into a modular architecture.

Manipulation of a sliding object

Abstract: Planning manipulation of an object free to slide on a surface is an important problem in many robotic applications. Physical analysis of the object's motion is made difficult by the absence of information about the distribution of support of the object on the surface, and of the resulting frictional forces. Here we describe a new approach to the analysis of sliding motion. We present results for the locus of centers of rotation for all possibie distributions of support. In one application to robotic manipulation, bounds on the distance an object must be pushed to come into alignment with a robot finger or a fence are determined.

A fuzzy logic approach to robotic path planning with obstacle avoidance

Abstract: Robotic path planning with obstacle avoidance is considered. The main objective of the proposed approach is to reduce planning time considerably for "real-time" applications with obstacles of arbitrary configuration. The concept of a minimum required joint motion envelope is introduced to facilitate the representation of the joint kinematic solutions. Near minimum time trajectories are generated through a phase plane analysis. If the planned path is obstructed, then the obstacle geometry is approximated and a suitable projection is found in joint space. A modified path is finally determined to avoid the obstacles. Fuzzy logic is employed to incorporate uncertainty into the algorithmic procedure. Preliminary investigations have been carried out using a PUMA 560 and its associated workspace.

On moving and orienting objects

Abstract: Many problems arising in the area of robotics are directly or indirectly motion related. In order to analyze such problems, it is necessary to incorporate the dynamics with the geometry in the mathematical formulation. With this in view, this thesis deals with two such problems--motion planning in the presence of uncertainty and the automated design of parts orienters. Motion planning for robots with errors in position measurement, velocity and time is considered and shown to be decidable in polynomial time for a large class of inputs. The robot model is then extended to include damping--a limited form of force sensing. Motion planning for point objects in three-dimensional scenes and robots with damping is shown to be PSPACE-hard. A simplified version of the same problem is shown to be PSPACE-complete. The problem of the automated design of parts orienters is rather closely related to motion planning. But the dynamics of the problem is so dominant that similar general formulations seem impossible. In this thesis, the alternative pursued is paradigm-by-paradigm analysis. Three paradigms are presented and analyzed--the "belt", for orienting convex polygons that are infinite in the third dimension, the "pan handler", for flat polygonal objects and the vibratory track for flat, convex polygons. Polynomial time algorithms are developed for the automated design of orienters in each of the paradigms.