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Randomized kinodynamic planning
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2001; 20; 378
, 2001
"... This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based ..."
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Cited by 626 (35 self)
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This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot’s environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot’s highdimensional configuration space. Kinodynamic planning is treated as a motionplanning problem in a higher dimensional state space that has both firstorder differential constraints and obstaclebased global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized pathplanning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 333 (20 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to ..."
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Cited by 187 (15 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
Kinodynamic Motion Planning
, 1993
"... : Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimaltime trajectory that goes from a start position and velocity to a goal position and velocity while avoidin ..."
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Cited by 133 (6 self)
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: Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimaltime trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be flown from a start to a goal, amidst polyhedral obstacles in 2D or 3D. While exact solutions to this problem are not known, we provide the first provably good approximation algorithm, and show that it runs in polynomial time. 1 An early version of this work appeared as [CDRX] 2 Computer Science Department, Cornell University, Ithaca, NY 14853 3 Computer Science Division, University of California, Berkeley, CA 94720 4 Computer Science Department, Duke Universit...
RealTime Robot Motion Planning Using Rasterizing Computer Graphics Hardware
 In Proc. SIGGRAPH
, 1990
"... We present a realtime robot motion planner that is fast andcomplete to a resolution. The technique is guaranteed to find a path if one exists at the resolution, and all paths returned are safe. The planner can handle any polyhedral geometry of robot and obstacles, including disjoint and highly conc ..."
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Cited by 120 (1 self)
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We present a realtime robot motion planner that is fast andcomplete to a resolution. The technique is guaranteed to find a path if one exists at the resolution, and all paths returned are safe. The planner can handle any polyhedral geometry of robot and obstacles, including disjoint and highly concave unions of polyhedra. The planner uses standard graphics hardware to rasterize configuration space obstacles into a series of bitmap slices, and then uses dynamic programming to create a navigation function (a discrete vectorvalued function) and to calculate paths in this rasterized space. The motion paths which the planner produces are minimal with respect to an L 1 (Manhattan) distance metric that includes rotation as well as translation. Several examples are shown illustrating the competence of the planner at generating planar rotational and translational plans for complex two and three dimensional robots. Dynamic motion sequences, including complicated and nonobvious backtracking so...
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
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Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems
 IEEE Transactions on Robotics and Automation
, 2001
"... Abstract — We introduce the notion of kinematic controllability for secondorder underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collisionfree trajectories between zero velocity states can be decoupled into the computationally simpler problems of ..."
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Cited by 78 (14 self)
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Abstract — We introduce the notion of kinematic controllability for secondorder underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collisionfree trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by timeoptimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collisionfree trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree 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 t ..."
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Cited by 68 (9 self)
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This paper focuses on the collisionfree 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 collisionfree 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 twopoint 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 carlike robots is described, along with implementation results for 12 robots.
Trajectory Planning in Dynamic Workspace: a `StateTime Space' Approach
, 1998
"... This report addresses trajectory planning in dynamic workspace, i.e. motion planning for a robot subject to dynamic constraints and moving in a workspace with moving obstacles. First is introduced the novel concept of statetime space, i.e. the state space of the robot augmented of the time dimens ..."
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Cited by 47 (4 self)
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This report addresses trajectory planning in dynamic workspace, i.e. motion planning for a robot subject to dynamic constraints and moving in a workspace with moving obstacles. First is introduced the novel concept of statetime space, i.e. the state space of the robot augmented of the time dimension. Like configuration space which is a tool to formulate path planning problems, statetime space is a tool to formulate trajectory planning in dynamic workspace problems. It permits to study the different aspects of dynamic trajectory planning, i.e. moving obstacles and dynamic constraints, in a unified way. Then this new concept is applied to the case of a carlike robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace. A neartimeoptimal approach that searches the solution trajectory over a restricted set of canonical trajectories is presented. These canonical trajectories are defined as having discrete and piecewise constant acceleration. Unde...
Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments
 International Journal of Robotics Research
, 1998
"... We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedo ..."
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Cited by 46 (14 self)
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We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight.