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Path Planning for Manipulation Environments through Interpolated Walks
Abstract
Manipulator robots working in changing environments need special path planners that provide good solutions in short times. In this work we describe a sample-based path planning algorithm that is suitable for such environments. Our approach is based on two points. Firstly, unlike most sampling techniques, we have defined a non-random local sampling which reduces the computational time greatly. Secondly, a set of interpolated walks is obtained through cubic splines which guarantee the smoothness and continuity of the walks. This path planning algorithm is part of a full intelligent manipulation system based on D vision
... This last characteristic is used to avoid local minima.Figure 12b shows the trajectories generated by the planner algorithm using W = 5, which signifies that each time a collision occurs, the local planner generates 5 new walks. Complete information concerning path planning can be found in [22]. After all these grasping components have been calculated, the grasp is simulated on a computer simulation tool and is finally executed in the robotic cell. ...
Humans decide how to carry out a spontaneous interactionwith an object by using the whole geometric information obtained from their eyes. The aim of this paper is to present how our object representation model MWS (Adán in Comput Vis Image Underst 79:281–307, 2000) can help a robot manipulator to make a single and reliable interaction. The contribution of this paper is particularly focused on thegrasp synthesis stage. The main idea is that the grasping system, through MWS, can use non-strict-local features of the contact points to find a consistent grasping configuration. The Direction Kernels (DK) concept, which is integrated into the MWS model, is used to define a set of candidate contact-points and interaction regions. The set of DK is a global feature which represents the principal normal vectors of the object and their relative weight in a three-connectivity mesh model. Our method calculates the optimal grasp points (which are ordered according to the quality function) for twofinger grippers, whilst maintaining the requirements of force closure and safety of the grasp. Our strategy has been extensively tested on real free-shape objects using a 6 DOF industrial robot.
We propose a new approach to robot path planning that consists of building and searching a graph connecting the local minima of a potential function defined over the robot's configuration space. A planner based on this approach has been implemented. This planner is consider ably faster than previous path planners and solves prob lems for robots with many more degrees of freedom (DOFs). The power of the planner derives both from the "good" properties of the potential function and from the efficiency of the techniques used to escape the local min ima of this function. The most powerful of these tech niques is a Monte Carlo technique that escapes local min ima by executing Brownian motions. The overall approach is made possible by the systematic use of distributed rep resentations (bitmaps) for the robot's work space and configuration space. We have experimented with the plan ner using several computer-simulated robots, including rigid objects with 3 DOFs (in 2D work space) and 6 DOFs (in 3D work space) and manipulator arms with 8, 10, and 31 DOFs (in 2D and 3D work spaces). Some of the most significant experiments are reported in this article.
A new motion planning method for robots in static workspaces is
presented. This method proceeds in two phases: a learning phase and a
query phase. In the learning phase, a probabilistic roadmap is
constructed and stored as a graph whose nodes correspond to
collision-free configurations and whose edges correspond to feasible
paths between these configurations. These paths are computed using a
simple and fast local planner. In the query phase, any given start and
goal configurations of the robot are connected to two nodes of the
roadmap; the roadmap is then searched for a path joining these two
nodes. The method is general and easy to implement. It can be applied to
virtually any type of holonomic robot. It requires selecting certain
parameters (e.g., the duration of the learning phase) whose values
depend on the scene, that is the robot and its workspace. But these
values turn out to be relatively easy to choose, Increased efficiency
can also be achieved by tailoring some components of the method (e.g.,
the local planner) to the considered robots. In this paper the method is
applied to planar articulated robots with many degrees of freedom.
Experimental results show that path planning can be done in a fraction
of a second on a contemporary workstation (≈150 MIPS), after learning
for relatively short periods of time (a few dozen seconds)
Probabilistic roadmap planners have been very successful in path planning for a wide variety of problems, especially applications involving robots with many degrees of freedom. These planners randomly sample the configuration space, building up a roadmap that connects the samples. A major problem is finding valid configurations in tight areas, and many methods have been proposed to more effectively sample these regions. By constructing a skeleton-like subset of the free regions of the workspace, these heuristics can be strengthened. The skeleton provides a concise description of the workspace topology and an efficient means of finding points with maximal clearance from the obstacles. We examine the medial axis as a skeleton, including a method to compute an approximation to it. The medial axis is a twoequidistant surface in the workspace. We form a heuristic for finding difficult configurations using the medial axis, and demonstrate its effectiveness in a planner for rigid objects in a three dimensional workspace.
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing.
Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background.
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We survey both old and new developments in the theory of algorithms in real
algebraic geometry -- starting from effective quantifier elimination in the
first order theory of reals due to Tarski and Seidenberg, to more recent
algorithms for computing topological invariants of semi-algebraic sets. We
emphasize throughout the complexity aspects of these algorithms and also
discuss the computational hardness of the underlying problems. We also describe
some recent results linking the computational hardness of decision problems in
the first order theory of the reals, with that of computing certain topological
invariants of semi-algebraic sets. Even though we mostly concentrate on exact
algorithms, we also discuss some numerical approaches involving semi-definite
programming that have gained popularity in recent times.
This article presents a method for determining smooth and time-optimal path constrained trajectories for robotic manipulators and investigates the performance of these trajectories both through simulations and experiments. The desired smoothness of the trajectory is imposed through limits on the torque rates. The third derivative of the path parameter with respect to time, the pseudo-jerk, is the controlled input. The limits on the actuator torques translate into state-dependent limits on the pseudo-acceleration. The time-optimal control objective is cast as an optimization problem by using cubic splines to parametrize the state space trajectory. The optimization problem is solved using the flexible tolerance method. The experimental results presented show that the planned smooth trajectories provide superior feasible time-optimal motion. © 2000 John Wiley & Sons, Inc.
1 Introduction and Overview.- 2 Configuration Space of a Rigid Object.- 3 Obstacles in Configuration Space.- 4 Roadmap Methods.- 5 Exact Cell Decomposition.- 6 Approximate Cell Decomposition.- 7 Potential Field Methods.- 8 Multiple Moving Objects.- 9 Kinematic Constraints.- 10 Dealing with Uncertainty.- 11 Movable Objects.- Prospects.- Appendix A Basic Mathematics.- Appendix B Computational Complexity.- Appendix C Graph Searching.- Appendix D Sweep-Line Algorithm.- References.
Randomized path planners have been successfully used to compute feasible paths for difficult planning problems. Such paths are typically computed without taking into account any optimality criteria and may contain many “jagged” segments because of the randomness involved in their generation. This paper presents a two-phase path planning algorithm, which uses a randomized planner to compute low-cost paths, and gradient descent to locally optimize these paths by minimizing a Hamiltonian function. The algorithm is tested on motion planning for a non-holonomic car-like robot. The results indicate that the two-phase approach is practical; however, gradient descent seems to be inefficient for the optimization of long paths.
This paper proposes a potential-based path planning algorithm of articulated robots with 2-DOF joints. The algorithm is an extension of a previous algorithm developed for 3-DOF joints. While 3-DOF joints result in a very straightforward potential minimization algorithm, 2-DOF joints are obviously more practical for active operations. The proposed approach computes repulsive force and torque between charged objects by using generalized potential model. A collision-free path can be obtained by locally adjusting the robot configuration to search for minimum potential config urations using these force and torque. The optimization of path safeness, through the innovative potential minimization algorithm, makes the proposed approach unique. In order to speedup the computation, a sequential planning strategy is adopted. Simulation results show that the proposed algorithm works well compared with the algorithm for 3-DOF joints, in terms of collision avoidance and computation efficiency.
This paper presents a novel approach to plan an optimal joint trajectory for a manipulator robot performing a compliant motion task. In general, a two-step scheme are deployed to find the optimal robot joint curve. Firstly, we approximate the functional and use Newton's iteration to numerically calculate the joint trajectory's intermediate discretized points, instead of solving a corresponding nonlinear, implicit Euler-Lagrange equation. Secondly, we interpolate these points to get the final joint curve in a way such that the motion constraints will always be sustained throughout the movement. An example of motion planning for a 4-degree-of-freedom robot WAM are given at the end of this paper
Fast path planning is achieved by a special representation of the robot and a two-phase path planning procedure. The representation consists of defining sets of body formations and arm postures whose number depends on complexity of the environment and the required resolution of path planning. In the off-line planning phase, the defined formations and postures are generated, and a 2D collision table is set up which specifies collision with obstacles of various defined body formations and arm postures. In the online planning phase, a graph search is carried out to find a sequence of adjacent formations and postures. Because the time consuming collision checking is done off-line, the online path finding is extremely fast. Path planning is essentially performed in the work space thus avoiding the costly mapping of obstacles into the C-space. The path planner has been implemented on a SUN workstation that controls a Puma 560 manipulator
We propose a novel single-shot motion-planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement, and the solution it produces can be easily and efficiently optimized. Furthermore, the algorithm can incorporate adaptive components, so the developer is not required to specify all the parameters of the random distributions involved, and the algorithm itself can adapt to the environment it is moving in. Proofs of the theoretical soundness of the algorithm are provided, as well as implementation details. Numerical comparisons with well-known algorithms illustrate its effectiveness.
Real world assembly sequences consists of multiple assembly steps, many of which can be performed in parallel. In practice this parallelism is often not exploited because of the complexity involved in avoiding collisions between all of the robots. In this paper we describe a simplified method of achieving smooth collision free paths for multiple robots within a single assembly workcell. Our method is simple because we exploit properties of B-splines to reduce the problem to path planning without moving robots. We develop a path planner to compute an initial linear path. Using that path as input, a trajectory generation tool creates a collision free path of any desired continuity. We exploit three properties of B-splines: (i) continuity for smooth paths, (ii) convex-hull for collision avoidance, and (iii) locality for dynamic course alteration without loss of continuity. In addition, our system runs in real-time, easily accommodating multiple robots. Finally, we describe a user level vi...
Motion planning using adaptive random walksOn-line Collision Avoidance for Multiple Robots Using B-Splines
- S Carpin
- G Pillonetto
S. Carpin and G. Pillonetto, "Motion planning using adaptive random walks", IEEE Transactions on Robotics, 21(1). pp. 129-136., 2005, [12] E. Paulos, "On-line Collision Avoidance for Multiple Robots Using B-Splines", Computer Science Technical Report. UC Berkeley. 1998