Showing papers on "Motion planning published in 1985"

Navigation for an intelligent mobile robot

Abstract: A navigation system is described for a mobile robot equipped with a rotating ultrasonic range sensor. This navigation system is based on a dynamically maintained model of the local environment, called the composite local model. The composite local model integrates information from the rotating range sensor, the robot's touch sensor, and a pre-learned global model as the robot moves through its environment. Techniques are described for constructing a line segment description of the most recent sensor scan (the sensor model), and for integrating such descriptions to build up a model of the immediate environment (the composite local model). The estimated position of the robot is corrected by the difference in position between observed sensor signals and the corresponding symbols in the composite local model. A learning technique is described in which the robot develops a global model and a network of places. The network of places is used in global path planning, while the segments are recalled from the global model to assist in local path execution. This system is useful for navigation in a finite, pre-learned domain such as a house, office, or factory.

Impedance Control: An Approach to Manipulation: Part III—Applications

Abstract: This three-part paper presents a unified approach to the control of a manipulator applicable to free motions, kinematically constrained motions, and dynamic interaction between the manipulator and its environment. In Part I the approach was developed from a consideration of the fundamental mechanics of manipulation. Part II presented techniques for implementing a desired manipulator impedance. In Part III a technique for choosing the impedance appropriate to a given application using optimization theory is presented. Based on a simplified analysis it is shown that if the task objective is to tradeoff interface forces and motion errors, the manipulator impedance should be proportional to the environmental admittance. An application of impedance control to unconstrained motion is presented. The superposition properties of nonlinear impedances are used to develop a real-time feedback control algorithm which permits a manipulator to avoid unpredictably moving objects without explicit path planning.

Distance functions and their application to robot path planning in the presence of obstacles

Abstract: An approach to robotic path planning, which allows optimization of useful performance indices in the presence of obstacles, is given. The main idea is to express obstacle avoidance in terms of the distances between potentially colliding parts. Mathematical properties of the distance functions are studied and it is seen that various types of derivatives of the distance functions are easily characterized. The results lead to the formulation of path planning problems as problems in optimal control and suggest numerical procedures for their solution. A simple numerical example involving a three-degree-of-freedom Cartesian manipulator is described.

Motion planning in the presence of moving obstacles

Abstract: This paper investigates the computational complexity of planning the motion of a body B in 2-D or 3-D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3-D dynamic movement problem is intractable even if B has only a constant number of degrees of freedom of movement. In particular, we prove the problem is PSPACE-hard if B is given a velocity modulus bound on its movements and is NP hard even if B has no velocity modulus bound, where in both cases B has 6 degrees of freedom. To prove these results we use a unique method of simulation of a Turing machine which uses time to encode configurations (whereas previous lower bound proofs in robotics used the system position to encode configurations and so required unbounded number of degrees of freedom). We also investigate a natural class of dynamic problems which we call asteroid avoidance problems: B, the object we wish to move, is a convex polyhedron which is free to move by translation with bounded velocity modulus, and the polyhedral obstacles have known translational trajectories but cannot rotate. This problem has many applications to robot, automobile, and aircraft collision avoidance. Our main positive results are polynomial time algorithms for the 2-D asteroid avoidance problem with bounded number of obstacles as well as single exponential time and nO(log n) space algorithms for the 3-D asteroid avoidance problem with an unbounded number of obstacles. Our techniques for solving these asteroid avoidance problems are novel in the sense that they are completely unrelated to previous algorithms for planning movement in the case of static obstacles. We also give some additional positive results for various other dynamic movers problems, and in particular give polynomial time algorithms for the case in which B has no velocity bounds and the movements of obstacles are algebraic in space-time.

Redefinition of the robot motion-control problem

Abstract: The objective of this paper is a redefinition of the robot control problem, based on (1) realistic models for the industrial robot as a controlled plant, (2) end-effector trajectories consistent with manufacturing applications, and (3) the need for end-effector sensing to compensate for uncertainties inherent to most robotic manufacturing applications. Based on extensive analytical and experimental studies, robot dynamic models are presented that have been validated over the frequency range 0 to 50 Hz. These models exhibit a strong influence of drive system flexibility, producing lightly damped poles in the neighborhood of 8 Hz, 14 Hz, and 40 Hz, all unmodeled by the conventional rigid-body multiple-link robot dynamic approach. The models presented also quantify the significance of non-linearities in the drive system, in addition to those well known in the linkage itself. Simulations of robot dynamics and motion controls demonstrate that existing controls coupled with effective path planning produce dynamic path errors that are acceptable for most manufacturing applications. Major benefits are projected, with examples cited, for use of end-effector sensors for position, force, and process control.

Planning a minimum-time trajectories for robot arms

Abstract: The minimum-time path for a robot arm has been a long-standing and unsolved problem of considerable interest. We present a general solution to this problem that involves joint-space tesselation, a dynamic time-scaling algorithm, and graph search. The solution incorporates full dynamics of movement and actuator constraints, and can be easily extended for joint limits and workspace obstacles, but is subject to the particular tesselation scheme used. The results presented show that, in general, the optimal paths are not straight lines, but rather curves in joint-space that utilize the dynamics of the arm and gravity to help in moving the arm faster to its destination. Implementation difficulties due to the tesselation and to combinatorial proliferation of paths are discussed.

Using backprojections for fine motion planning with uncertainty

Abstract: This paper outlines a method for planning motions in the presence of uncertainty. Tasks are modelled as geometrical goals in configuration space. The planning process consists of determining regions from which particular motions are guaranteed to successfully reach a desired goal. 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.

A study of the clash detection problem in robotics

Abstract: To solve the clash detection problem we must decide whether a collision will occur between any pair of objects from a set of objects with known shapes and motions. We have considered three methods for performing clash detection: in the first we sample the motion at a finite number of times and perform interference detection at each time; in the second we create models of the shapes and their motions in space-time, and look for intersections between these four-dimensional entities; and in the third we create models of the volumes swept out by the objects. This paper is a brief, comparative study of these three methods, and includes some details of our experiments with the first two methods as implemented in a geometric modelling system.

Natural decomposition of free space for path planning

Abstract: This paper describes an algorithm that decomposes the free space into nonoverlapping geometric-shaped primitives suitable for path planning. Given a set of polygonal obstacles in space, the algorithm first decomposes concave obstacles into connecting convex obstacles in order to have a uniform obstacle representation, which facilitates later processing. The neighborhood relations among these Convex obstacles are identified and then used to locate critical "channels" and "passage regions" in the free space, and to localize the influence of obstacles on free space description. The free space is then decomposed into nonoverlapping geometric-shaped primitives where channels connect passage regions. The channels are similar to the generalized cones presented in Brooks [1]. The passage regions are represented as convex polygons. Based on this mixed representation of free space, the path planning algorithm can plan path trajectories inside the channels and passage regions. The perimeter of the channels and passage regions associated with the planned path provides the boundaries of the path that the mobile robot must stay within during path execution.

Minimum-time path planning for robot arms and their dynamics

Abstract: Despite its close relationship to robot arm dynamics, conventional path planning does not take it into account, leading to the possible underutilization of the robot's capabilities. The authors have developed a minimum-time path-planning method in joint space taking into consideration robot arm dynamics as well as other realistic constraints. The main differences between this method and others are: (1) an absolute tolerance in the path deviation at each corner point can be specified; (2) local upper bounds on joint accelerations are derived from the arm dynamics so as to nearly fully utilize robot's capabilities; and (3) a set of local optimization problems, one at every local corner point, replaces the global minimum-time problem, thus making the minimum-time path-planning problem simpler and easier to solve. The method is applied to the path planning of the first three joints of the Unimation PUMA 600 series robot arm, using its simulator on a DEC VAX-11/780. The results show significant improvements in the total traveling time in addition to the ease and simplicity obtained from the decomposition of the global problem into a set of local optimization problems.

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 time history of position and velocity) due to the complexity and nonlinearity of the manipulator dynamics, control of manipulators has been conventionally divided into two subproblems, namely path planning and path tracking, which are then separately and independently solved. This may result in mathematically tractable solutions but cannot 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 has a simple structure allowing for on-line implementation with inexpensive mini- or microcomputers, and offers a near minimum time-fuel (NMTF) solution, thus enabling manipulators to perform nearly up to their maximum capability and efficiency. As a demonstrative example, we have simulated the proposed control method with a dynamic model of the Unimation PUMA 600 series manipulator on a DEC VAX-11/780. The simulation results agree with the expected high performance nature of the control method.

A Voronoi method for the piano-movers problem

Abstract: We describe work in progress toward a polynomial-time algorithm for the classical movers' problem With 6 degrees of freedom. Rotations are represented as a certain 3-dimensional subset of the space of quaternions. This representation gives rise to algebraic constraints on the allowable configurations of the moving object. We define a generalized Voronoi diagram in the configuration space and show that a subset of the diagram, consisting of zero and one dimensional manifolds, can be constructed in polynomial time, and paths found along it. While this subset of the diagram is not always sufficient for path planning, the triangulation of 1- dimensional manifolds can be used as the basis of a complete path planning algorithm by adding other 1-manifolds.

Computational Geometry and Motion Planning

Abstract: Research and development work in robotics and industrial automation has created a need for good motion planning algorithms for collision avoidance; this in turn has stimulated research on the inherent computational geometry of motion planning. The purpose of this paper is to survey some recent algorithms and complexity results for motion planning, placing particular emphasis on computational geometry issues. A brief discussion of a variety of the many different types of problems that arise in the context of motion planning is included, as many of these problems involve geometric questions. The main focus of the paper, however, is on the following problem and its variants: Given descriptions of an object and a collection of obstacles in 2 or 3-dimensional space, and given the initial and desired final configuration for the object, find a collision-free trajectory that moves the object to its goal or determine that no such trajectory exists.

Selection of Near-Minimum Time Geometric Paths for Robotic Manipulators

Abstract: A number of trajectory or path planning algorithms exist for calculating the joint positions, velocities, and torques which will drive a robotic manipulator along a given geometric path in minimum time. However, the time depends upon the geometric path, so the traversal time of the path should be considered again for geometric planning. There are algorithms available for finding minimum distance paths, but even when obstacle avoidance is not an issue minimum (Cartesian) distance is not necessarily equivalent to minimum time. In this paper, we have derived a lower bound on the time required to move a manipulator from one point to another, and determined the form of the path which minimizes this lower bound. As a numerical example, we have applied the path solution to the first three joints of the Bendix PACS arm, a cylindrical robot. This example does indeed demonstrate that the derived approximate solutions require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths, i.e. those paths for which joint positions qi are given by qi = ai + bi?.

Coordinating the motions of robot arms in a common workspace

Abstract: A time/space planning system to coordinate the actions of two robot manipulators for transfer movements in a "sparse" environment is reported here The collision avoidance reasoning guarantees that arms will arrive safely at their destination by temporally delaying or by altering the path of one arm End effectors are constrained to follow elliptical motions The performance of the system is sufficient in normal circumstances to drive an execution module in real time with tool tip speeds about three inches per second

An efficient and simple motion planning algorithm for a ladder moving in two-dimensional space amidst polygonal barriers (extended abstract)

Abstract: We present a relatively simple algorithm which runs in time O(n2log n) for the above mentioned problem. The algorithm is an optimized variant of the decomposition technique of the configuration space of the ladder, due to Schwartz and Sharir. The algorithm is based on some ideas which may be exploited to improve the efficiency of existing motion-planning algorithms for other more complex robot systems.

On motion planning with six degrees of freedom: Solving the intersection problems in configuration space

Abstract: The Movers' problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. The classical formulation of the three-dimensional Movers' problem is as fellows: given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a contineous, collision-free path taking P from some initial configuration to a desired goal configuration. The six degree or freedom Movers' problem may be transformed into a point, navigation problem in a six-dimensional configuration space (called C-Space). The C-Space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the closure of three operators which (i) slide along 5-dimensional level C-surfaces parallel to C-Space obstacles; (ii) slide along 1- to 4-dimensional intersections of level C-surfaces; and (iii) jump between 6-dimensional obstacles. We show how to construct and represent C-surfaces and their intersection manifolds. We also demonstrate how to intersect trajectories with the boundaries of C

Redundant Sensors for Mobile Robot Navigation

Abstract: : Redundant sensors are needed on a mobile robot so that the accuracy with which it perceives its surroundings can be increased. Sonar and infrared sensors are used here in tandem, each compensating for deficiencies in the other. The robot combines the data from both sensors to build a representation which is more accurate than if either sensor were used alone. Another representation, the curvature primal sketch, is extracted from this perceived workspace and is used as the input to two path planning programs: one based on configuration space and one based on a generalized cone formulation of free space. (Author).

Simulation of path planning for a system with vision and map updating

Abstract: This paper represents part of the ongoing research into an Intelligent Mobile Autonomous System (IMAS). An intermediate path planning subsystem (Navigator), for the hierarchy of IMAS, is presented which operates in completely known, partially known, and completely unknown environments. Information is passed from a sensor to the Navigator via the "Cartographer" which performs map updating. The interaction and performance of these subsystems are demonstrated in a simulation of the IMAS hierarchy.

A proximity metric for continuum path planning

Abstract: The problem of planning motions of robot manipulators and similar mechanical devices in the presence of obstacles is one of keen interest to the artificial intelligence community. Most of the algorithms previously reported for solving such problems have been combinatorial algorithms, which work by partitioning the problem domain continuum into a finite set of equivalence classes, and applying combinatorial search algorithms to plan transitions among them. However, the few continuum algorithms that have been reported, which do not rely on such a partitioning, have shown greater promise when applied to problems of complexity equivalent to that of planning a true manipulator motion. This is true even though the heuristics employed in these continuum algorithms have been extremely simple in nature. A significant barrier to the development of more refined heuristics for use in continum algorithms is the uncertainty over how to characterise the proximal relationship between rigid bodies. In this paper, a new measurement function is reported which permits such characterisation. An introduction is made to a new type of path planning algorithm which this function makes possible, which promises to significantly increase the capabilities of continuum path planning software.

Minimum time robot path planning in the presence of obstacles

Abstract: An approach to minimum time robotic path planning in the presence of obstacles is given. It is formulated in an optimal control context with obstacle avoidance expressed in terms of the distances between potentially colliding parts. Procedures for computing the distances between general part shapes in three-dimensional space are discussed. Numerical examples involving manipulators operating in two and three-dimensional workspaces are described.

Robotic hands with rheological surfaces

Abstract: The purpose of this paper is to analyze, in some depth, the processes involved in the manipulation of solid objects using robotic hands. Such an analysis has implications for design, control, and motion planning. We make a case for the use of finger surfaces which have a distributed compliance and show how such surfaces may be realized by fluid filled pods. The arguments given are based on an analysis of the complexity of the kinematic programming problem, an enumeration of the number of independent feedback control channels necessary for achieving a firm grasp and an examination of frictional forces. We emphasize the necessity of dealing with models which lead to well-posed problems throughout the grasping process and point out some of the ways that earlier models lead to ambiguous situations.

On the complexity of reachability and motion planning questions (extended abstract)

Abstract: In this paper we consider from a theoretical viewpoint the complexity of some reachability and motion planning questions. Specifically, we are interested in determining which generalizations of the basic mover's problem result in computationally intractable problems. It has been shown that for any set of motion-planning problems with bounded degree of freedom, there is a polynomial-time algorithm to solve the motion-planning problem (although the degree of the polynomial may be large), but the two most basic generalizations to the problem, multiple movable obstacles and conformable objects, result in much harder problems. It has been shown that the warehouseman's problem is P-space hard: in this paper we show that the reachability problem for one of the simplest types of conformable objects, a two-dimensional linear (“robot arm”) linkage, is P-space complete. In addition, we demonstrate some motion-planning problems that take exponential time.

Algorithmic motion planning in robotics: Coordinated motion of several disks amidst polygonal obstacles

Abstract: Given k ≥ 2 circular disks D 1 , D 2 ...D k in a 2-dimensional region bounded by a finite set of polygonal obstacles, an algorithm to determine the existence of a collision free coordinated motion of the disks is given. The time complexity is shown to be O(nk} where n is the number of edges composing the walls. This algorithm is believed to be optimal.

Multi-goal real-time global path planning for an autonomous land vehicle using a high-speed graph search processor

Abstract: This paper presents a fast and powerful global path planning subsystem for an autonomous land vehicle (ALV). It addresses its relation with a complete hierarchical planner and describes its real-time implementation.

A hierarchical-orthogonal-space approach to collision-free path planning

Abstract: We present a methodology for 3-D collision-free path planning in which planning is done in the 3-orthogonal 2-D projections of a 3-D environment. Suboptimal path searching is done in each of the 3 orthogonal 2-D subspaces using primitive path segments. A hierarchical path searching method is introduced to speed up the search process. This approach lends applications to spatial planning in environments where no a priori knowledge is assumed. The three orthogonal 2-D projections can be readily obtained from 3 orthogonal cameras in simple environments.

Approximate optimum paths of robot manipulators under realistic physical constraints

Abstract: A method is developed for planning the point-to-point path that the manipulator may adopt to minimize a specified performance index, under the realistic physical constraints on Joint torques, accelerations, velocities and position limits. The purpose of such path planning is either to provide the best input for the manipulator controller or to evaluate the arm performance for various designs. Because there is no analytic function available for describing the optimum path, cubic spline functions are proposed for an approximation. For a selected number of polynomial segments, the flexible polyhedron search is used to search for the optimum path arrangement. During the search period, it is often necessary to convert an infeasible arrangement into a feasible one. Methods for these required conversions have been studied. The number of concatenated polynomials is increased until there is no significant improvement on the approximation. Computer programs have been written to implement the algorithm.

Trajectory Planning In Time-Varying Environments, 1: TPP = PPP + VPP

Abstract: In this paper, we present a novel approach to solving the trajectory planning problem (TPP) in time-varying environments. The essence of our approach lies in a decom-position of the TPP into two sub-problems: (i) planning the path to avoid collision with the static obstacles, and then (ii) planning the velocity along the path to avoid collision with the moving obstacles. We call the first sub-problem, the path planning problem (PPP), and the second, the velocity plan-ning problem (VPP). Thus, our decomposition is summarized by the equation TPP = PPP VPP. We use a variation of an existing approach to solve the PPP. Furthermore, we transform the VPP to a 2-dimensional PPP in path-time space. The resulting 2-dimensional PPP is then solved to determine the collision-free velociy profile.