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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 620 (36 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 336 (21 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 194 (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
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 83 (20 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.
Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators
 Algorithmica
, 1995
"... shortest path, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd a minimaltime trajectory that goes from a start state to a goal state while avoiding obstacles by a speeddependent safetymargin and respecting dynamics bounds. In [1] we develop ..."
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Cited by 79 (9 self)
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shortest path, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd a minimaltime trajectory that goes from a start state to a goal state while avoiding obstacles by a speeddependent safetymargin and respecting dynamics bounds. In [1] we developed a provably good approximation algorithm for the minimumtime trajectory problem for a robot system with decoupled dynamics bounds (e.g., a point robot in R 3). This algorithm di ers from previous work in three ways. It is possible (1) to bound the goodness of the approximation by an error term �(2) to polynomially bound the computational complexity of our algorithm � and (3) to express the complexity as a polynomial function of the error term. Hence, given the geometric obstacles, dynamics bounds, and the error term, the algorithm returns a solution that isclose to optimal and requires only a polynomial (in ( 1)) amount of time. We extend the results of [1] in two ways. First, we modifyittohalve the exponent inthe polynomial bounds from 6d to 3d, so that that the new algorithm is O c d N 1 3d, where N is the geometric complexity of the obstacles and c is a robotdependent constant. Second, the new algorithm nds a trajectory that matches the optimal in time with an factor sacri ced in the obstacleavoidance safety margin. Similar results hold for polyhedral Cartesian manipulators in polyhedral environments. The new results indicate that an implementation of the algorithm could be reasonable, and a preliminary implementation has been done for the planar case.
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 65 (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 50 (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 Trajectory Planning with Dynamic Constraints: a `StateTime Space' Approach
, 1993
"... This paper addresses dynamic trajectory planning which is defined as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e. with moving obstacles. To begin with, we propose the novel concept of statetime space as a tool to formulate dynamic trajectory ..."
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Cited by 43 (5 self)
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This paper addresses dynamic trajectory planning which is defined as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e. with moving obstacles. To begin with, we propose the novel concept of statetime space as a tool to formulate dynamic trajectory planning problems. The statetime space of a robot is its state space augmented of the time dimension. It permits to study the different aspects of dynamic trajectory planning in a unified way. Thus the constraints imposed by both the moving obstacles and the dynamic constraints can be represented by static forbidden regions of statetime space. Besides a trajectory maps to a curve in statetime space hence dynamic trajectory planning simply consists in finding a curve in statetime space. Then we apply this new concept in order to determine a timeoptimal trajectory for a carlike robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace. We present a...
Differentially Constrained Mobile Robot Motion Planning in State Lattices
, 2008
"... We present an approach to the problem of differentially constrained mobile robot motion planning in arbitrary cost fields. The approach is based on deterministic search in a specially discretized state space. We compute a set of elementary motions that connects each discrete state value to a set of ..."
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Cited by 39 (4 self)
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We present an approach to the problem of differentially constrained mobile robot motion planning in arbitrary cost fields. The approach is based on deterministic search in a specially discretized state space. We compute a set of elementary motions that connects each discrete state value to a set of its reachable neighbors via feasible motions. Thus, this set of motions induces a connected search graph. The motions are carefully designed to terminate at discrete states, whose dimensions include relevant state variables (e.g., position, heading, curvature, and velocity). The discrete states, and thus the motions, repeat at regular intervals, forming a lattice. We ensure that all paths in the graph encode feasible motions via the imposition of continuity constraints on state variables at graph vertices and compliance of the graph edges with a differential equation comprising the vehicle model. The resulting state lattice permits fast full configuration space cost evaluation and collision detection. Experimental results with research prototype rovers demonstrate that the planner allows us to exploit the entire envelope of vehicle maneuverability in rough terrain, while featuring realtime performance. C ○ 2009 Wiley Periodicals, Inc. 1.
SamplingBased Motion Planning with Differential Constraints

, 2005
"... Since differential constraints which restrict admissible velocities and accelerations of robotic systems are ignored in path planning, solutions for kinodynamic and nonholonomic planning problems from classical methods could be either inexecutable or inefficient. Motion planning with differential c ..."
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Cited by 29 (4 self)
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Since differential constraints which restrict admissible velocities and accelerations of robotic systems are ignored in path planning, solutions for kinodynamic and nonholonomic planning problems from classical methods could be either inexecutable or inefficient. Motion planning with differential constraints (MPD), which directly considers differential constraints, provides a promising direction to calculate reliable and efficient solutions. A large amount of recent efforts have been devoted to various samplingbased MPD algorithms, which iteratively build search graphs using sampled states and controls. This thesis addresses several issues in analysis and design of these algorithms. Firstly, resolution completeness of path planning is extended to MPD and the first quantitative conditions are provided. The analysis is based on the relationship between the reachability graph, which is an intrinsic graph representation of a given problem, and the search graph, which is built by the algorithm. Because of sampling and other complications, there exist mismatches between these two graphs. If a solution exists in the reachability graph, resolution complete algorithms must construct a solution path encoding the solution or its approximation in the search graph