C-space Obstacles Research Articles

SPAM for a Manipulator by Best Next Move in Unknown Environments

We propose a SPAM (simultaneous planning and mapping) technique for a manipulator-type robot working in an uncertain environment via a novel Best Next Move algorithm. Demands for a smart decision to move a manipulator such as humanoid arms in uncertain or crowded environments call for a simultaneous planning and mapping technique. In the present work, we focus more on rapid map generation rather than global path search to reduce ignorance level of a given environment. The motivation is that the global path quality will be improved as the ignorance level of the unknown environment decreases. The 3D sensor introduced in the previous work has been improved for better mapping capability and the real-time rehearsal idea is used for c-space cloud point generation. Captured cloud points by 3D sensors, then, create an instantaneous c-space map whereby the Best Next Move algorithm directs the local motion of the manipulator. The direction of the Best Next Move utilizes the gradient of the density distribution of the k-nearest-neighborhood sets in c-space. It has a tendency of traveling along the direction by which the point clouds spread in space, thus rendering faster mapping of c-space obstacles possible. The proposed algorithm is compared with a sensor-based algorithm such as sensor-based RRT for performance comparison. Performance measures, such as mapping efficiency, search time, and total number of c-space point clouds, are reported as well. Possible applications include semiautonomous telerobotics planning and humanoid arm path planning.

Motion Path Control of Multi-DOF Handling Manipulator in Industrial Field Based on Vision and C-Space Obstacle Avoidance

In order to realize the intelligentization of the multi-DOF handling manipulator in the industrial field, this paper presents a motion path control approach which combines the vision based identification and localization and C-space (Configuration space) based obstacle avoidance planning. The objects in the image captured by CCD camera can be extracted by gray processing, background subtraction, binarization, and edge detecting, the work pieces and the obstacles can be matched based on roundness and squareness, and then the coordinates of above objects can be obtained by parallax and coordinate conversion. In addition, both the source and destination coordinates in C-space can be obtained by mapping these configurations position and orientation into C-space, and the motion path can be automatically generated by variable step A* search in free area which is built based on solid manipulator model, then the handling work can be finished and obstacle avoidance can also be realized. The results of simulation and experiment demonstrate the scientificalness and effectiveness of this control approach.

On the construction of discretized configuration space of manipulators

In this research, we study the construction of configuration space (C-space) of manipulators. The proposed approach is based upon precomputing the global topology of a robot's free space, and consists of an offline phase and an online phase. In the offline phase, a C-space obstacle database (COD) for a given robot is developed in which the C-space obstacle (C-obstacle) maps are stored and indexed by the cells of the workspace; in the online phase when the same robot is operated in a real environment, those maps whose indices match the real obstacle cells are identified and then extracted from the COD. The superposition of these maps forms forbidden region in operation. This proposed approach is a generic one and can be applied to manipulators with arbitrary kinematic structures and geometries. The construction of the COD, which is generally the most time-consuming step, is implemented in the offline phase, and the online computing only involves the identification of the components matching the COD indices. Therefore, this proposed approach for C-space construction can be realized in a real-time online fashion and is especially suitable for robot manipulation under dynamic operations. We carry out analyses on several types of manipulators to verify and demonstrate the feasibility and efficiency of the proposed approach.

A real-time path planning approach without the computation of Cspace obstacles

An important concept proposed in the early stage of robot path planning field is the shrinking of the robot to a point and meanwhile expanding of the obstacles in the workspace as a set of new obstacles. The resulting grown obstacles are called the Configuration Space (Cspace) obstacles. The find-path problem is then transformed into that of finding a collision free path for a point robot among the Cspace obstacles. However, the research experiences obtained so far have shown that the calculation of the Cspace obstacles is very hard work when the following situations occur: 1. both the robot and obstacles are not polygons and 2. the robot is allowed to rotate. This situation is even worse when the robot and obstacles are three dimensional (3D) objects with various shapes. Obviously a direct path planning approach without the calculation of the Cspace obstacles is strongly needed. This paper presents such a new real-time robot path planning approach which, to the best of our knowledge, is the first one in the robotic community. The fundamental ideas are the utilization of inequality and optimization technique. Simulation results have been presented to show its merits.

Interference-free polyhedral configurations for stacking

This paper uses a configuration space (c-space) based method to compute interference-free configuration for stacking polyhedral sheet metal parts. This work forms the interference analysis module of a stacking planner developed by us. Parts in a stack should not interfere with each other and should also satisfy stability, grasping, and stacking plan feasibility related constraints. We present two techniques to speed up the expensive step of c-space obstacle computation. The first technique identifies orientation intervals (for a convex pair of solids) within which the topology of face-edge-vertex graph of an obstacle stays the same. Within this interval, c-space obstacle geometry for one orientation can be extrapolated from obstacle geometry for another orientation. Our experiments show that extrapolation takes an order of magnitude less than the time taken to compute an obstacle from scratch. The second technique computes near optimal interference-free positions for a discrete orientation without having to compute the complete c-space obstacle. Our experiments show that, for complex sheet metal parts, less than 0.1% of the convex component pairs are evaluated in order to compute an interference-free configuration. We describe a configuration space-based method to compute a list of interference-free configurations that can be tested to see if they satisfy the above mentioned constraints. The cost function is a weighted sum of components that penalize floor space utilization and height of center of gravity of parts. The algorithm is able to pick nested stacks that tend to be stable and compact without having to explicitly enumerate features that can be nested. It is also able to accommodate flanges in holes to reduce the value of the user specified cost function. We use three test parts to illustrate the effect of the two techniques to speed up c-space obstacle computation. We also show the stacking plans generated for three different values of the weighting parameter in the cost function used by the stacking planner.

A heuristic approach to robot path planning based on task requirements using a genetic algorithm

In order to enhance integration between CAD and robots, wer propose a scheme to plan kinematically feasible paths in the presence of obstacles based on task requirements. Thus, the feasibility of a planned path from a CAD system is assured before the path is sent for execution. The proposed scheme uses a heuristic approach to deal with a rather complex search space, involving high-dimensional C-space obstacles and task requirements specified in Cartesian space. When the robot is trapped by the local minimum in the potential field related to the heuristic, a genetic algorithm is then used to find a proper intermediate location that will guide it to escape out of the local minimum. For demonstration, simulations based on using a PUMA-typed robot manipulator to perform different tasks in the presence of obstacles were conducted. The proposed scheme can also be used for mobile robot planning.

Fast Computation of the C-Space of Convex 2D Algebraic Objects

Collision-free paths for a robot are commonly obtained in con figuration space. The major problem with this approach is the computation of the boundary of the configuration space ob stacles. While many results have been reported for polygonal environments, the general case of arbitrary object shape has received little attention in the literature so far. This article presents a new method for tackling this problem in the case of objects for which the boundaries consist of segments of pa rameterized algebraic curves. A fast numerical algorithm that computes the boundaries of the C-space obstacles in param eterized form is developed. The major result is that initially subdividing the segments guarantees the convergence and lim its the computational costs of the applied interval-subdivision Newton method. This makes it possible to compute the exact C-space for this more general class of objects. Finally, two examples with convex objects solved by our implementation are given.

Generation of Configuration Space Obstacles: Moving Algebraic Surfaces

We present an algebraic algorithm to generate the boundary of configuration space obstacles arising from the translatory motion of curved convex objects among curved convex obsta cles. Both the boundaries of the objects and obstacles are given by patches of algebraic surfaces. Further, we consider obtaining compliant motion paths where a curved convex object with fixed orientation moves in continuous contact with another curved convex obstacle in three-dimensional space. We also give a method to obtain a piecewise algebraic, ap proximate geodesic path on a curved convex C-space obstacle.

A search algorithm for motion planning with six degrees of freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The “Movers'” problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Movers' problem: Given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration. This paper describes an implementation of a complete algorithm (at a given resolution) for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem 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 five-dimensional level C-surfaces parallel to C-space obstacles; (ii) slide along one- to four-dimensional intersections of level C-surfaces; and (iii) jump between six-dimensional obstacles. These operators are employed by a best-first search algorithm in C-space. We will discuss theoretical properties of the algorithm, including completeness (at a resolution). This paper describes the heuristic search, with particular emphasis on the heuristic strategies that evaluate local geometric information. At the heart of this paper lie the design and implementation of these strategies for planning paths along level C-surfaces and their intersection manifolds, and for reasoning about motions with three degrees of rotational freedom. The problems of controlling the interaction of these strategies, and of integrating diverse local experts for geometric reasoning provide an interesting application of search to a difficult domain with significant practical implications. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.