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)

This paper presents a new randomized roadmap method for motion planning for many dof robots that can be used to obtain high quality roadmaps even when C-space is crowded. The main novelty in our approach is that roadmap candidate points are chosen on C-obstacle surfaces. As a consequence, the roadmap is likely to contain difficult paths, such as those traversing long, narrow passages in C-space. The approach can be used for both collision-free path planning and for manipulation planning of contact tasks. Experimental results with a planar articulated 6 dof robot show that, after preprocessing, difficult path planning operations can often be carried out in less than a second. 1 Introduction Automatic motion planning has application in many areas such as robotics, virtual reality systems, and computeraided design. Although many different motion planning methods have been proposed, most are not used in practice since they are computationally infeasible except for some restricted cases, e...

A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not exhibit the local minima which plague the potential field method. Unlike decompositional and algebraic techniques, Laplace’s Equation is very well suited to computation on massively parallel architectures. 1

Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot' s configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilistically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the "goodness" of the robot's free space, we show that the running time only grows as the absolute value of the logarithm of the probability of failure that we are willing to tolerate. We also show that it increases at a reasonable rate as the space goodness degrades. In the last section we suggest directions for future research.

Abstract This paper presents a comparative evaluation of different dis-tance metrics and local planners within the context of probabilistic roadmap methods for motion planning. Both C-space andWorkspace distance metrics and local planners are considered. The study concentrates on cluttered three-dimensionalWorkspaces typical, e.g., of mechanical designs. Our results include recommendations for selecting appropriate combinationsof distance metrics and local planners for use in motion planning methods, particularly probabilistic roadmap methods. Wefind that each local planner makes some connections than none of the others do-- indicating that better connectedroadmaps will beconstructed using multiple local planners. We propose a new local planning method we call rotate-at-s that outperforms the commonstraight-line in C-space method in crowded environments. 1

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

problematic and forces the human VE participant to attend to the interface and its control knobs in addition to or instead of the goals and constraints of the task at hand. If the intention of the human VE participant is, e.g., to observe some object X, then allowing him or her to simply tell the system, Show me object X is a more direct and productive interface. This is an instance of task level interaction. In earlier work we characterized the levels of abstraction at which one can interact with virtual objects and processes, and we described the varying access panels one obtains (5). Here we will describe a system for specifying behaviors for virtual cameras in terms of task level goals and constraints. As in our earlier work on camera control (6, 7), we make task level control available as well as enabling various direct manipulation metaphors. This paper describes a framework for exploring intelligent camera controls in a 3D virtual environment. It presents a methodology for ...

We present a new approach to the multi-robot path planning problem, where a number of robots are to change their positions through feasible motions in the same static environment. Rather than the usual decoupled planning, we use a coordinated approach. As a result we can show that the method is probabilistically complete, that is, any solvable problem will be solved within a finite amount of time. A data-structure storing multi-robot motion is built in two steps. First, a roadmap is constructed for just one robot. For this we use the probabilistic path planner, which guarantees that the approach can be easily applied to different robot types. In the second step, a number of these simple roadmaps are combined into a roadmap for the composite robot. This data-structure can be used for retrieving multi-robot paths. We have applied the method to car-like robots, and simulation results are presented which show that problems involving up to five car-like robots in complex environments are solved successfully in computation times in the order of seconds, after a preprocessing step (the construction of the data-structure) that consumes, at most, a few minutes. Such a preprocessing step however needs to be performed just once, for a

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.

this paper, we applied the proposed methodology to various problems such as occlusions avoidance, constraints on the field of view (i.e., keeping an object inside view), 3D contact in a cluttered environment (i.e., obstacle avoidance). This method as been previously used for singularities and joint limits avoidance [11]. A similar approach has been proposed by Nelson and Khosla. It consists of minimizing an objective function which realizes a compromise between the visual task (a target tracking using a camera mounted on the end effector of a manipulator) and the avoidance of kinematic singularities, joint limits singularities but also with some other constraints on the field of view, the focus measure [12]. This function is used by exploiting the robot degrees of freedom which are redundant with respect to the visual task. However, the resulting camera motions can produce major perturbations in the visual servoing since they are generally not compatible with the regulation to zero of the selected image features. The next section of this paper, taken from [11], recalls the application of the task function approach to visual servoing and the expression of the resulting control law. Section 3 describes the approach proposed to dynamic sensor planning. We finally present real time experimental results dealing with various robotic tasks. These results have been obtained using an eye-in-hand system composed of a camera mounted on the end-effector of a six d.o.f Zebra Zero robot.