Showing papers on "Motion planning published in 1988"

The complexity of robot motion planning

Abstract: The Complexity of Robot Motion Planning makes original contributions both to robotics and to the analysis of algorithms. In this groundbreaking monograph John Canny resolves long-standing problems concerning the complexity of motion planning and, for the central problem of finding a collision free path for a jointed robot in the presence of obstacles, obtains exponential speedups over existing algorithms by applying high-powered new mathematical techniques.Canny's new algorithm for this "generalized movers' problem," the most-studied and basic robot motion planning problem, has a single exponential running time, and is polynomial for any given robot. The algorithm has an optimal running time exponent and is based on the notion of roadmaps - one-dimensional subsets of the robot's configuration space. In deriving the single exponential bound, Canny introduces and reveals the power of two tools that have not been previously used in geometric algorithms: the generalized (multivariable) resultant for a system of polynomials and Whitney's notion of stratified sets. He has also developed a novel representation of object orientation based on unnormalized quaternions which reduces the complexity of the algorithms and enhances their practical applicability.After dealing with the movers' problem, the book next attacks and derives several lower bounds on extensions of the problem: finding the shortest path among polyhedral obstacles, planning with velocity limits, and compliant motion planning with uncertainty. It introduces a clever technique, "path encoding," that allows a proof of NP-hardness for the first two problems and then shows that the general form of compliant motion planning, a problem that is the focus of a great deal of recent work in robotics, is non-deterministic exponential time hard. Canny proves this result using a highly original construction.John Canny received his doctorate from MIT And is an assistant professor in the Computer Science Division at the University of California, Berkeley. The Complexity of Robot Motion Planning is the winner of the 1987 ACM Doctoral Dissertation Award.

Sensor fusion in certainty grids for mobile robots

Abstract: A numeric representation of uncertain and incomplete sensor knowledge called certainty grids was used successfully in several recent mobile robot control programs developed at the Carnegie-Mellon University Mobile Robot Laboratory (MRL). Certainty grids have proven to be a powerful and efficient unifying solution for sensor fusion, motion planning, landmark identification, and many other central problems. MRL had good early success with ad hoc formulas for updating grid cells with new information. A new Bayesian statistical foundation for the operations promises further improvement. MRL proposes to build a software framework running on processors onboard the new Uranus mobile robot that will maintain a probabilistic, geometric map of the robot's surroundings as it moves. The certainty grid representation will allow this map to be incrementally updated in a uniform way based on information coming from various sources, including sonar, stereo vision, proximity, and contact sensors. The approach can correctly model the fuzziness of each reading and, at the same time, combine multiple measurements to produce sharper map features; it can also deal correctly with uncertainties in the robot's motion. The map will be used by planning programs to choose clear paths, identify locations (by correlating maps), identify well-known and insufficiently sensed terrain, and perhaps identify objects by shape. The certainty grid representation can be extended in the time dimension and used to detect and track moving objects. Even the simplest versions of the idea allow us to fairly straightforwardly program the robot for tasks that have hitherto been out of reach. MRL looks forward to a program that can explore a region and return to its starting place, using map "snapshots" from its outbound journey to find its way back, even in the presence of disturbances of its motion and occasional changes in the terrain.

Optimal robot plant planning using the minimum-time criterion

Abstract: A path planning technique is presented which produces time-optimal manipulator motions in a workspace containing obstacles. The full nonlinear equations of motion are used in conjunction with the actuator limitations to produce optimal trajectories. The Cartesian path of the manipulator is represented with B-spline polynomials, and the shape of this path is varied in a manner that minimizes the traversal time. Obstacle avoidance constraints are included in the problem through the use of distance functions. In addition to computing the optimal path, the time-optimal open-loop joint forces and corresponding joint displacements are obtained as functions of time. The examples presented show a reduction in the time required for typical motions. >

Combined observer-controller synthesis for uncertain dynamical systems with applications

Abstract: Control of a class of nonlinear/uncertain systems is discussed using a variable-structure systems approach. Observations of the states of such systems is also considered. The natural extension to an observer-controller design is illustrated using a computer simulation example of a theta -r manipulator. Next, the problem of path planning is addressed using a combined observer-controller strategy. The aspects of hardware implementation of the proposed observer-controller are then analyzed. >

Motion planning in the presence of movable obstacles

Abstract: Motion planning algorithms have generally dealt with motion in a static environment, or more recently, with motion in an environment that changes in a known manner. We consider the problem of finding collision-free motions in a changeable environment. That is, we wish to find a motion for an object where the object is permitted to move some of the obstacles. In such an environment the final positions of the movable obstacles may or may not be part of the goal. In the case where the final positions of the obstacles are unspecified, the motion planning problem is shown to be NP-hard. An algorithm that runs in O(n2logn) time after O(n3log2n) preprocessing time is presented when the object to be moved is polygonal and there is only one movable polygonal obstacle in a polygonal environment of complexity O(n). In the case where the final positions of the obstacles are specified the general problem is shown to be PSPACE-hard and an algorithm is given when there is one movable obstacle with the same preprocessing time as the previous algorithm but with O(n2) query time.

Region filling operations with random obstacle avoidance for mobile robots

Abstract: The article presents a new topic in path planning for mobile robots, region filling. which involves a sweeping operation to fill a whole region with random obstacle avoidance. The approaches for global strip filling and local path searching driven by sensory data procedures are developed. A computer graphic simulation is used to verify the filling strategy available. The research was developed from the program for the design of a robot lawn mower. However, the solution appears generic. The significance is that a problem of wide application and generic solutions for general autonomous mobile robots have been developed.

Planning constrained motion

Abstract: We consider the motion planning problem for a point constrained to move along a path with radius of curvature at least one. The point moves in a two-dimensional universe with polygonal obstacles. We show the decidability of the reachability question: “Given a source placement (position and direction pair) and a target placement, is there a curvature-constrained path from source to target avoiding obstacles?” The decision procedure has time and space complexity 2o(poly(n, m)) wheren is the number of corners andm is the number of bits required to specify the position of corners.

A practical exact motion planning algorithm for polygonal objects amidst polygonal obstacles extended abstact

Abstract: A general and simple algorithm is presented which computes the set FP of all free configurations for a polygonal object I (with m edges) which is free to translate and/or to rotate but not to intersect another polygonal object E. The worst-case time complexity of the algorithm is O(m/sup 3/n/sup 3/ log mn), which is close to optimal. FP is a three-dimensional curved object which can be used to find free motions within the same time bounds. Two types of motion have been studied in some detail. Motion in contact, where I remains in contact with E, is performed by moving along the faces of the boundary of FP. By partitioning FP into prisms, it is possible to compute motions when I never makes contact with E. In this case, the theoretical complexity does not exceed O(m/sup 6/n/sup 6/ alpha (mn)) but it is expected to be much smaller in practice. In both cases, pseudo-optimal motions can be obtained with a complexity increased by a factor log mn.<>

Planning collision-free trajectories in time-varying environments: a two-level hierarchy

Abstract: Global geometric algorithms for trajectory planning are used in conjunction with a local avoidance strategy. Simulations have been developed for a mobile robot in the plane among stationary and moving obstacles. Essentially, the robot has a geometric planner that provides a coarse trajectory (the path and the velocity along it), which may be modified by a (low-level) local avoidance module if sensors detect obstacles in the vicinity of the robot. This hierarchy makes effective use of the complementarity between global trajectory planning and local obstacle avoidance. >

A variational dynamic programming approach to robot-path planning with a distance-safety criterion

Abstract: An approach to robot-path planning is developed by considering both the traveling distance and the safety of the robot. A computationally-efficient algorithm is developed to find a near-optimal path with a weighted distance-safety criterion by using a variational calculus and dynamic programming (VCDP) method. The algorithm is readily applicable to any factory environment by representing the free workspace as channels. A method for deriving these channels is also proposed. Although it is developed mainly for two-dimensional problems, this method can be easily extended to a class of three-dimensional problems. Numerical examples are presented to demonstrate the utility and power of this method. >

Path planning using a potential field representation

Abstract: An approach to two-dimensional as well as three-dimensional findpath problems that divides each problem into two steps is presented. Rough paths are found based only on topological information. This is accomplished by assigning to each obstacle an artificial potential similar to electrostatic potential to prevent the moving object from colliding with the obstacles, and then locating minimum-potential valleys. The paths defined by the minimum-potential valleys are modified to obtain an optimal collision-free path and orientations of the moving object along the path. Three algorithms are given to accomplish this second step. These three algorithms based on potential fields are nearly complete in scope, and solve a large variety of problems. >

On grasping and coordinated manipulation by a multifingered robot hand

Abstract: Two problems in the study of multifingered robot hands are considered, namely grasp planning and the determination of coordinated control laws with point contact models. using the dual notions of grasp stability and manipulability, and a procedure previously developed for task modeling, the structure grasp quality measures are defined. These measures are then integrated to devise a grasp planning algorithm. Based on the assumption of point contact models, a computed-torque-like control algorithm is developed for the coordinated manipulation of a multifingered robot hand. This control algorithm, which takes into account both the dynamics of the object and the dynamics of the hand, is computationally effective and can be generalized to allow rolling motion of the object with respect to the fingertip. >

The complexity of planar compliant motion planning under uncertainty

Abstract: We consider the computational complexity of planning compliant motions in the plane, given geometric bounds on the uncertainty in sensing and control. We can give efficient algorithms for generating and verifying compliant motion strategies that are guaranteed to succeed as long as the sensing and control uncertainties lie within the specified bounds. We also consider the case where a compliant motion plan is required to succeed over some parametric family of geometries. While these problems are known to be intractable in 3D, we identify tractable subclasses in the plane.

A paradigm for incorporating vision in the robot navigation function

Abstract: The authors present a paradigm for combining vision with motion planning. It turns out that extensive modifications of so-called tactile algorithms are needed to take full advantage of the additional sensing capabilities, while not sacrificing the algorithm convergence. Different design principles can be introduced that result in algorithm versions exhibiting different styles of behavior and producing different paths, without, in general, being superior to each other. >

Trajectory planning in robotic continuous-path applications

Abstract: Trajectory planning of robot motions for continuous-path operations is formulated in configuration space, resorting to the intrinsic properties of the path traced by point of the end effector. It is shown that, by referring the orientation of the end effector to a unique orthogonal frame defined at every point of the aforementioned path, a systematic procedure for trajectory planning in configuration space is derived. The computations required to determine the angular velocity and angular acceleration of the path frame reduce to computing the Darboux vector of the path and its time derivative. >

Motion planning among time dependent obstacles

Abstract: In this paper we study the problem of motion planning in the presence of time dependent, i.e. moving, obstacles. More specifically, we will consider the problem: given a bodyB and a collection of moving obstacles inD-dimensional space decide whether there is a continuous, collision-free movement ofB from a given initial position to a target position subject to the condition thatB cannot move any faster than some fixed top-speedc. As a discrete, combinatorial model for the continuous, geometric motion planning problem we introduce time-dependent graphs. It is shown that a path existence problem in time-dependent graphs is PSPACE-complete. Using this result we will demonstrate that a version of the motion planning problem (where the obstacles are allowed to move periodically) is PSPACE-hard, even ifD=2, B is a square and the obstacles have only translational movement. ForD=1 it is shown that motion planning is NP-hard. Furthermore we introduce the notion of thec-hull of an obstacle: thec-hull is the collection of all positions in space-time at which a future collision with an obstacle cannot be avoided. In the low-dimensional situationD=1 andD=2 we develop polynomial-time algorithms for the computation of thec-hull as well as for the motion planning problem in the special case where the obstacles are polyhedral. In particular forD=1 there is aO(n lgn) time algorithm for the motion planning problem wheren is the number of edges of the obstacle.

Motion planning for a mobile robot with a kinematic constraint

Abstract: The motion planning problem is discussed for a mobile robot with a kinematic constraint, that is, the number of its degrees of freedom is less than the dimension of its configuration space. Addressing first the local problem of turning in a corridor, it is shown that sliding continuously on the outer wall in a turn constitutes a canonical contract trajectory, in the sense that if it is not safe, there cannot be another safe trajectory with no backing-up maneuver. For the case in which no smooth trajectory exists, some simple maneuvers are proposed. A heuristic path-planning algorithm based on a decomposition of free space into cones connected by turns is then presented. It is shown how this approach can be used within the more realistic framework of an actual mobile robot at work by implementing the results as a set of rules of behavior for the robot. >

Method and apparatus for path planning

Abstract: A method and apparatus for path planning are presented. Path planning involves propagating cost waves in a configuration space representation of a task space. A space variant metric and budding are used for cost wave propagation. The disclosed method and apparatus are readily adaptable to robots with n degrees of freedom.

The kinematics of motion planning for multilegged vehicles over uneven terrain

Abstract: A motion planning algorithm for uneven-terrain locomotion for a multilegged vehicle is described. The algorithm has been developed based on the vehicle/terrain kinematic relationships. The vehicle model is chosen from a hexapod vehicle, named the Adaptive Suspension Vehicle (ASV), which has been constructed at Ohio State University (OSU) and is currently being tested. A simple body-regulation plan has been designed based on the local slope of the terrain and should increase the safety and adaptability of the vehicle. The local terrain is estimated by using the support points of the supporting legs and proximity information from the transfer legs. The adjustment of the position and dimensions of the constrained working volume for each leg, which increases the vehicle stability over sloped terrain, is discussed. The algorithm has been implemented in simulation on a PDP-11/70 minicomputer, from which test results are given. >

Path planning among moving obstacles using spatial indexing

Abstract: A method is presented for planning a path in the presence of moving obstacles. Given a set of polygonal moving obstacles, a path is generated for a mobile robot that navigates in the two-dimensional plane. Time is included as one of the dimensions of the model world. This allows the moving obstacles to be regarded as stationary in the extended world. For a solution to be feasible, the robot must not collide with any other moving obstacles and must navigate within the predetermined range of velocity, acceleration, and centrifugal force. A spatial index is used to facilitate geometric search for the path-planning task. Computer simulation results are presented to illustrate the feasibility of this approach. >

Motion planning for robot arm manipulators with proximity sensing

Abstract: The problem of sensor-based path planning for robot arm manipulators operating among unknown obstacles of arbitrary shape is considered. It has been known that, in principle, algorithms with proven convergence can be designed for planar and simple three-dimensional robot arms operating under such conditions. However, implementation of these algorithms presents a variety of hardware and algorithmic problems related to covering the robot arm with a sensitive skin, processing data from large arrays of sensors, and designing algorithms for step-by-step motion planning based on limited information. The authors describe the hardware and the lower-level control algorithms of a system for robot motion planning in an uncertain environment and summarize results of experiments with the system. >

The complexity of fine motion planning

Abstract: We study the complexity of fine motion planning for robots with position measurement and damping. A reduction from fine motion planning with position measurement only to the ``classical piano mover''s problem'''' is developed, thereby showing it to be feasible in polynomial time. We then show that deciding the existence of fine motion plans for robots with damping in three dimensional scenes is PSPACE-hard and, with a view to finding the cause for the jump in the complexity, we identify a restricted subclass of the PSPACE-hard problem that is PSPACE-complete. Finally, we show how to restrict this subclass to permit polynomial time algorithms for the problems in it.

A probabilistic approach to collision-free robot path planning

Abstract: A method was developed that takes into consideration the size and shape of the obstacles as well as the distance from the robot's current position to the obstacles. The workspace is divided into a finite number of cubes. An obstacle is represented by the set of cubes it occupies. The probability of each cube becoming a dead end is calculated under the assumption that both the starting and destination points are randomly located in the workspace with a known distribution. These probabilities are used to determine an optimal robot path that minimizes some cost associated with the path. Several illustrative examples are presented. The method is intended to be used for 3-D problems and is simple enough to be implemented for online robot path planning. >

Learning expert systems for robot fine motion control

Abstract: The authors present a learning expert system which enables a robot to acquire fine motion skills automatically. The system follows the paradigm of Expert Assisted Robot Skill Acquisition (EARSA) proposed by the authors (1987). EARSA is mainly concerned with the self-discovery of skills by a robot in conjunction with the transfer of human skills to a robot and emphasizes the distinctive difference in perceptual and physical capabilities between a human and a robot. The authors review the theory and mechanism of EARSA, describe the robot fine motion skill learning algorithm formulated on the basis of EARSA, and present the details of simulation on the robot learning of two-dimensional peg-hole insertion skills. The results of simulation indicate the dramatic improvement of performance as a result of skill learning. >

A fast path-planning algorithm by synchronizing modification and search of its path graph (mobile robots)

Abstract: Determination of the shortest collision-free path for a mobile robot between start and goal positions in a workspace is central to the design of an autonomous mobile robot. The authors present a feasible path-planning algorithm which runs on the quadtree representation using a path graph. The quadtree representing the workspace is obtained from fast conversion of a real image taken through a camera on the ceiling. The quadtree integrates both obstacle regions and other regions in the workspace with its hierarchical structure in positioning. By using this hierarchical structure, the mobile robot is reduced to a point and then the forbidden regions where the robot cannot enter into are also understood in the quadtree. Hence, the algorithm can select the shortest collision-free path from the quadtree, i.e. a line between two given positions. Experimental results show that the proposed algorithm is superior to certain conventional algorithms with respect to calculation time. >

World representation and path planning for a mobile robot

Abstract: This paper is related to the problem of navigation of a mobile robot amidst obstacles. In order to easily take into account any modification of the environment, we propose a very simple representation of the obstacles, based on the use of rectangles, as well as a matrix description of the spatial relationships between the obstacles. We also present a path planner based on a A* algorithm, the features of which are specifically designed for our world of rectangles. The cost function takes into account both the length of the path and the number of turns. Some experimental results and implementation details are also given in this paper.

Accessibility: a new approach to path planning among moving obstacles

Abstract: A study is performed of the problem of planning a collision-free path for a robot in a time-varying environment. It is assumed that an obstacle moves along a known path. The formulation also allows the destination point (the point to be reached) to move along a predetermined path. A concept of 'accessibility' from a point to a moving object is introduced and is used to determine a collision-free path. An environment which contains some uncertainty in which the robot needs to see and possibly plan an alternative path is also considered. The ability to deal with moving obstacles is useful in a variety of visual tasks such as the navigation of an autonomous vehicle and the interaction between robot arms. >

On-line generation of collision-free trajectories for multiple robots

Abstract: An online algorithm is proposed to test interferences and generate collision-free trajectories for the motions of loosely coordinated multiple robot manipulators controlled independently by means of PD (proportional differential) controllers. A hierarchical multiple-robot-control architecture is proposed. The approach is demonstrated by simulation studied. >