Free Configuration Space Research Articles

Path Connectivity of the Free Space

This paper revisits the notion of free configuration space and reviews some of its path-connectivity-related properties. The literature on motion planning reveals at least three different definitions for the free configuration space of a robot in the presence of obstacles. This paper shows that, assuming regularity of both object and obstacles, those three definitions are equivalent. We show that the three definitions regularize the free space and therefore prevent the existence of “thin bits,” or low-dimensional strata. The paper concludes by discussing a series of properties regarding the existence and smoothability of contact-free paths between pairs of configurations.

Research on Quantitative Model of Path Planning for Mobile Robots

According to free configuration space, the skeleton graph of working environment of mobile robots was constructed. The length of link of skeleton graph was quantified according the actual length of pathway and presented with quantitative length matrix. The width of link of skeleton graph was quantified by the width rate of pathway and robot body, and presented with quantitative width matrix. For a pathway with width changing, the width was quantified according to the minimum width of the pathway. For multiply pathways between two vertexes, the pathways were merged into one pathway. In dynamic environment, the matrix value of link was set to -1 for a pathway with obstacles. In Dijkstra algorithm, the coordination path planning of multiply robots was implemented by comparing the remaining capacity of pathway width and the robot body.

PRM과 포텐셜 필드 기법에 기반한 다자유도 머니퓰레이터의 충돌회피 경로계획

The collision-free path of a manipulator should be regenerated in the real time to achieve collision safety when obstacles or humans come into the workspace of the manipulator. A probabilistic roadmap (PRM) method, one of the popular path planning schemes for a manipulator, can find a collision-free path by connecting the start and goal poses through the roadmap constructed by drawing random nodes in the free configuration space. The path planning method based on the configuration space shows robust performance for static environments which can be converted into the off-line processing. However, since this method spends considerable time on converting dynamic obstacles into the configuration space, it is not appropriate for real-time generation of a collision-free path. On the other hand, the method based on the workspace can provide fast response even for dynamic environments because it does not need the conversion into the configuration space. In this paper, we propose an efficient real-time path planning by combining the PRM and the potential field methods to cope with static and dynamic environments. The PRM can generate a collision-free path and the potential field method can determine the configuration of the manipulator. A series of experiments show that the proposed path planning method can provide robust performance for various obstacles.

Reachability-based analysis for Probabilistic Roadmap planners

In the last fifteen years, sampling-based planners like the Probabilistic Roadmap Method ( prm) have proved to be successful in solving complex motion planning problems. While theoretically, the complexity of the motion planning problem is exponential in the number of degrees of freedom, sampling-based planners can successfully handle this curse of dimensionality in practice. We give a reachability-based analysis for these planners which leads to a better understanding of the success of the approach. This analysis compares the techniques based on coverage and connectivity of the free configuration space. The experiments show, contrary to general belief, that the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a refined neighbor selection strategy, a hybrid sampling strategy, and a more powerful local planner, leading to a considerable speed-up.

Translating a convex polyhedron over monotone polyhedra

Let S be a collection of geometric objects in R 3 , and let P be another geometric object in R 3 . The free configuration space of P with respect to S is the set of all possible placements of P so that P does not intersect the set S. Finding combinatorial and computational bounds for the computation of the free configuration space is a currently active area of research in computational geometry. We show in this paper that the free configuration space of a convex polyhedron P freely translating over a polyhedral terrain having a convex projection T can be computed in O( nm+ k+ t) time in the worst case, where m and n are the number of faces of P and T, respectively, k denotes the size of the output and t is a parameter whose value could be, at most, O( n 2 mlog n).

Using Artificial Neural Networks (ANNs) in Detection Methodologies. First Detection Results Concerning a DMDP Antenna Structure

The objective of this paper is to present detection results, produced from experiments in a Dual Mode Dual Polarity (DMDP) antenna structure, using a general detection methodology based on Statistics and Artificial Neural Networks (ANNs), in order to detect possible abnormalities within the structure. The antenna is supposed in three states (healthy, minus2bolts, minus1mass). Several experiments, both on healthy and damaged DMDP antenna structure, were carried out in a free configuration space i.e. the structure is suspended with elastic strings, so that it has rigid body suspension frequencies. Frequency Response Functions (FRFs) were recorded and used to detect the abnormalities. A simple identifier for all frequencies is proposed and statistically studied. This identifier is then used by the proposed methodology to compute the diagnosis. The diagnosis performance is 100% for all the treated experiments (in laboratory).

Pipes, Cigars, and Kreplach: the Union of Minkowski Sums in Three Dimensions

Let Ω be a set of pairwise-disjoint polyhedral obstacles in ℝ3 with a total of n vertices, and let B be a ball in ℝ3. We show that the combinatorial complexity of the free configuration space ${cal F}$ of B amid Ω, i.e., (the closure of) the set of all placements of B at which B does not intersect any obstacle, is O(n 2+ε), for any ε > 0; the constant of proportionality depends on ε. This upper bound almost matches the known quadratic lower bound on the maximum possible complexity of ${cal F}$. The special case in which Ω is a set of lines is studied separately. We also present a few extensions of this result, including a randomized algorithm for computing the boundary of ${cal F}$ whose expected running time is O(n 2+ε),for any ε > 0.

Sensor-based probabilistic roadmaps: experiments with an eye-in-hand system

We present a real implemented eye-in-hand test-bed system for sensor-based collision-free motion planning for articulated robot arms. The system consists of a PUMA 560 with a triangulation-based area-scan laser range finder (the eye) mounted on its wrist. The framework for our planning approach is inspired by recent motion planning research for the classical model-based case (known environment) and incrementally builds a roadmap that represents the connectivity of the free configuration space, as the robot senses the physical environment. We present some experimental results with our sensor-based planner running on this real test-bed. The robot is started in completely unknown and cluttered environments. Typically, the planner is able to reach (planning as it senses) the goal configuration in about 7-25 scans (depending on the scene complexity), while avoiding collisions with the obstacles throughout.

Motion Planning for a Convex Polygon in a Polygonal Environment

We study the motion-planning problem for a convex m -gon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the three-dimensional space of all free placements of P in Q ) in time that is near-quadratic in mn , which is nearly optimal in the worst case. The algorithm is also conceptually simple. Previous solutions were incomplete, more expensive, or produced only part of the free configuration space. Combining our solution with parametric searching, we obtain an algorithm that finds the largest placement of P in Q in time that is also near-quadratic in mn . In addition, we describe an algorithm that preprocesses the computed free configuration space so that reachability queries can be answered in polylogarithmic time.

The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots

This paper proposes a novel and global approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. Given an initial configuration of the robot, the problem is to find a reachable configuration that corresponds to a desired position and orientation of the end-effector. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the connected component of the free configuration space of the manipulator in a finite graph like structure. The point-to-point inverse kinematics problem is then solved using this roadmap. We provide completeness results for our algorithm. Our implementation of SEARCH is an efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

Motion Planning in Environments with Low Obstacle Density

We present a simple and efficient paradigm for computing the exact solution of the motion planning problem in environments with a low obstacle density. Such environments frequently occur in practical instances of the motion planning problem. The complexity of the free space for such environments is known to be linear in the number of obstacles. Our paradigm is a new cell decomposition approach to motion planning and exploits properties that follow from the low density of the obstacles in the robot's workspace. These properties allow us to decompose the workspace, subject to some constraints, rather than to decompose the higher-dimensional free configuration space directly. A sequence of uniform steps transforms the workspace decomposition into a free space decomposition of asymptotically the same size. The approach leads to nearly optimal O(n \log n) motion planning algorithms for free-flying robots with any fixed number of degrees of freedom in workspaces with low obstacle density.

Multilevel Path Planning for Nonholonomic Robots Using Semiholonomic Subsystems

We present a new and complete multilevel approachfor solving path- planning problems for nonholonomic robots. At the first level, a path is found that disrespects (some of) the nonholonomic constraints. At each of the next levels, a new path is generated by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the previous level. At the final level, all nonholonomic constraints are respected. We present two techniques for these transformations. The first, which we call the pick and link technique, repeatedly picks pieces from the given path, and tries to replace them by more feasible ones. The second technique restricts the free configuration space to a "tube" around the given path, and a road map that captures the free-space connectivity within this tube is constructed by the prob abilistic path planner. From this road map we retrieve a new, more feasible path. In the intermediate levels, we plan paths for what we refer to as semiholonomic subsystems. Such systems are obtained by taking real (physical) systems, and removing some of their nonholonomic constraints. In this paper, we apply the scheme to carlike robots pulling trail ers, that is, tractor-trailer robots. In this case, the real system is the tractor-trailer robot, and the ignored constraints in the semiholo nomic subsystems are the kinematic ones on the trailers. These are the constraints of rolling without slipping, on the trailer's wheels. Experimental results are given that illustrate the time efficiency of the resulting planner. In particular, we show that using the multilevel scheme leads to significantly better performance (in computation time and path shape) than direct transformations to feasible paths.

On Translational Motion Planning of a Convex Polyhedron in 3-Space

Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1,...,Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free placements) of B can be represented as the complement of the union of the Minkowski sums $P_i=A_i\oplus (-B)$, for i= 1,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log k), and that it can be $\Omega(nk\alpha(k))$ in the worst case, where n is the total complexity of the individual Minkowski sums P1,...,Pk. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log k log n).

A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment

We consider the problem of planning the motion of an arbitraryk-sided polygonal robotB, free to translate and rotate in a polygonal environmentV bounded byn edges. We present an algorithm that constructs a single component of the free configuration space ofB in timeO((kn)2+ź), for any ź>0. This algorithm, combined with some standard techniques in motion planning, yields a solution to the underlying motion-planning problem, within the same running time.

Connectivity graphs on two‐dimensional surfaces and their application in robotics

AbstractThe problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analysed via the corresponding connectivity graph. For two‐degree‐of‐freedom robots, the free configuration space presents a two‐dimensional (2D) surface—a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc.) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the subspace, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms capable of on‐line motion planning in an environment with unknown obstacles of arbitrary shapes. This makes the method distinct from other techniques, which require complete information, algebraic representation of space geometry, and off‐line computation.

Connectivity Graphs on Two-Dimensional Surfaces and Their Application in Robotics

The problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analyzed via the corresponding connectivity graph. For some two-and three-dimensioned (2D and 3D) robots, the free configuration space presents a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the sub-space, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms which can be used for real-time sensor-based motion planning in an environment with unknown obstacles of arbitrary shapes.