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26
Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 251 (15 self)
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AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of twoinput systems can be converted into this form. I.
Efficient Collision Detection for Animation and Robotics
, 1993
"... We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two ..."
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Cited by 108 (19 self)
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We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...
Path planning using Laplace’s equation
, 1990
"... 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 ..."
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Cited by 96 (8 self)
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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
MultiAUV control and adaptive sampling in Monterey Bay
 IEEE Journal of Oceanic Engineering
, 2004
"... Abstract—Operations with multiple autonomous underwater vehicles (AUVs) have a variety of underwater applications. For example, a coordinated group of vehicles with environmental sensors can perform adaptive ocean sampling at the appropriate spatial and temporal scales. We describe a methodology for ..."
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Cited by 57 (15 self)
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Abstract—Operations with multiple autonomous underwater vehicles (AUVs) have a variety of underwater applications. For example, a coordinated group of vehicles with environmental sensors can perform adaptive ocean sampling at the appropriate spatial and temporal scales. We describe a methodology for cooperative control of multiple vehicles based on virtual bodies and artificial potentials (VBAP). This methodology allows for adaptable formation control and can be used for missions such as gradient climbing and feature tracking in an uncertain environment. We discuss our implementation on a fleet of autonomous underwater gliders and present results from sea trials in Monterey Bay in August, 2003. These atsea demonstrations were performed as part of the Autonomous Ocean Sampling Network (AOSN) II project. Index Terms—Adaptive sampling, autonomous underwater vehicles (AUVs), cooperative control, formations, gradient climbing, underwater gliders. I.
A Random Approach to Motion Planning
, 1992
"... The motion planning problem asks for determining a collisionfree path for a robot amidst a set of obstacles. In this paper we present a new approach for solving this problem, based on the construction of a random network of possible motions, connecting the source and goal configuration of the ro ..."
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Cited by 53 (24 self)
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The motion planning problem asks for determining a collisionfree path for a robot amidst a set of obstacles. In this paper we present a new approach for solving this problem, based on the construction of a random network of possible motions, connecting the source and goal configuration of the robot.
An Opportunistic Global Path Planner
, 1993
"... In this paper we describe a robot path planning algorithm that constructs a global skeleton of freespace by incremental local methods. The curves of the skeleton are the loci of maxima of an artificial potential field that is directly proportional to distance of the robot from obstacles. Our method ..."
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Cited by 51 (9 self)
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In this paper we describe a robot path planning algorithm that constructs a global skeleton of freespace by incremental local methods. The curves of the skeleton are the loci of maxima of an artificial potential field that is directly proportional to distance of the robot from obstacles. Our method has the advantage of fast convergence of local methods in uncluttered environments, but it also has a deterministic and efficient method of escaping local extremal points of the potential function. We first describe a general roadmap algorithm, for configuration spaces of any dimension, and then describe specific applications of the algorithm for robots with two and three degrees of freedom.
RealTime Replanning in HighDimensional Configuration Spaces Using Sets of Homotopic Paths
, 2000
"... ..."
Neural Network Dynamics for Path Planning and Obstacle Avoidance
, 1995
"... A model of a topologically organized neural network of a Hopfield type with nonlinear analog neurons is shown to be very effective for path planning and obstacle avoidance. This deterministic system can rapidly provide a proper path, from any arbitrary start position to any target position, avoiding ..."
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Cited by 35 (0 self)
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A model of a topologically organized neural network of a Hopfield type with nonlinear analog neurons is shown to be very effective for path planning and obstacle avoidance. This deterministic system can rapidly provide a proper path, from any arbitrary start position to any target position, avoiding both static and moving obstacles of arbitrary shape. The model assumes that an (external) input activates a target neuron, corresponding to the target position, and specifies obstacles in the topologically ordered neural map. The path follows from the neural network dynamics and the neural activity gradient in the topologically ordered map. The analytical results are supported by computer simulations to illustrate the performance of the network. 1 This work has been accepted by Neural Networks (March 1994). 1 1 Introduction Human motor control reveals a versatility of function and economy of space, that is yet beyond the reach of robots. One of the important themes of research in the fi...
A Motion Planner for Multiple Mobile Robots
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1990
"... We describe an algorithm for planning the motions of several mobile robots which share the same workspace. Each robot is capable of independent translational motion in two dimensions, and the workspace contains polygonal obstacles. The algorithm computes a path for each robot which avoids all obstac ..."
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Cited by 16 (0 self)
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We describe an algorithm for planning the motions of several mobile robots which share the same workspace. Each robot is capable of independent translational motion in two dimensions, and the workspace contains polygonal obstacles. The algorithm computes a path for each robot which avoids all obstacles in the workspace as well as the other robots. It is guaranteed to find a solution if one exists. The algorithm takes a cell decomposition approach, where the decomposition used is based on the idea of a product operation defined on the cells in a decomposition of a twodimensional free space. We are implementing this algorithm for the case of two robots as part of ongoing research into useful algorithms for tasklevel programming of the RobotWorld 1 system.
Analog VLSI for Robot Path Planning
 Journal of VLSI Signal Processing
, 1994
"... : Analog VLSI provides a convenient and highperformance engine for robot path planning. Laplace's equation is a useful formulation of the path planning problem; however, digital solutions are very expensive. Since high precision is not required an analog approach is attractive. A resistive network ..."
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Cited by 14 (3 self)
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: Analog VLSI provides a convenient and highperformance engine for robot path planning. Laplace's equation is a useful formulation of the path planning problem; however, digital solutions are very expensive. Since high precision is not required an analog approach is attractive. A resistive network can be used to model the robot's domain with various boundary conditions for the source, target, and obstacles. A gradient descent can then be traced through the network by comparing node voltages. We built two analog CMOS VLSI chips to investigate the feasibility of this technique. Design issues included the choice of resistive element, tessellation of the domain, programming of the network and readout of the settled network. Both chips can be connected to a standard VME bus interface to permit their use as coprocessors in otherwise digital systems. Keywords: analog VLSI, Laplace's equation, resistive networks, path planning. 1 Introduction Robot path planning is an important area of st...