Results 1  10
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162
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 336 (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.
Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2001
"... We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete statespace asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetrypreserving kinetic shaping and feedbackcontrolled di ..."
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Cited by 129 (31 self)
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We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete statespace asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetrypreserving kinetic shaping and feedbackcontrolled dissipation for statespace stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.
Visual Servoing via Navigation Functions
 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION
, 2002
"... This paper presents a framework for visual servoing that guarantees convergence to a visible goal from almost every initially visible configuration while maintaining full view of all the feature points along the way. The method applies to first and second order fully actuated plant models. The solut ..."
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Cited by 60 (7 self)
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This paper presents a framework for visual servoing that guarantees convergence to a visible goal from almost every initially visible configuration while maintaining full view of all the feature points along the way. The method applies to first and second order fully actuated plant models. The solution entails three components: a model for the "occlusionfree" configurations; a change of coordinates from image to model coordinates; and a navigation function for the model space. We present three example applications of the framework, along with experimental validation of its practical efficacy.
Automatic synthesis of multiagent motion tasks based on ltl specifications
 IN PROCEEDINGS OF THE 43RD IEEE CONFERENCE ON DECISION AND CONTROL
, 2004
"... In this paper we propose a methodology for automatically synthesizing motion task controllers based on Linear Temporal Logic (LTL) specifications. The proposed design of the underlying multiagent controllers possess a special structure that allows for implicit satisfaction of basic liveness and s ..."
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Cited by 48 (4 self)
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In this paper we propose a methodology for automatically synthesizing motion task controllers based on Linear Temporal Logic (LTL) specifications. The proposed design of the underlying multiagent controllers possess a special structure that allows for implicit satisfaction of basic liveness and safety specifications. The resulting closed loop system is of hybrid nature combining the continuous dynamics of the underlying system with the automatically synthesized switching logic that enforces the LTL specification. The effectiveness of the proposed scheme is verified through nontrivial computer simulations.
A Feedback Stabilization and Collision Avoidance Scheme for Multiple Independent Nonholonomic Nonpoint Agents
, 2005
"... A navigation functions’ based methodology, established previously for decentralized navigation of multiple holonomic agents, is extended to address the problem of decentralized navigation of multiple nonholonomic agents. In contrast to our previous work, each agent does not require any knowledge ab ..."
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Cited by 47 (28 self)
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A navigation functions’ based methodology, established previously for decentralized navigation of multiple holonomic agents, is extended to address the problem of decentralized navigation of multiple nonholonomic agents. In contrast to our previous work, each agent does not require any knowledge about the velocities and the desired destinations of the other members of the team. Furthermore, the control inputs are the acceleration and rotational velocity of each vehicle, coping in this way with realistic dynamics of classes of mechanical systems. Asymptotic stability is guaranteed by LaSalle’s Invariance Principle for nonsmooth systems. The collision avoidance and global convergence properties are verified through simulations.
Closed Loop Navigation for Multiple Holonomic Vehicles
 Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems
, 2002
"... In this paper an online multirobot navigation methodology is presented, extending the concept of navigation functions from the single robot to the multiple robot domain. An appropriate measure of the distance from bad sets, suitable for multirobot navigation is introduced. ..."
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Cited by 41 (21 self)
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In this paper an online multirobot navigation methodology is presented, extending the concept of navigation functions from the single robot to the multiple robot domain. An appropriate measure of the distance from bad sets, suitable for multirobot navigation is introduced.
Dynamic assignment in distributed motion planning with local information
 IEEE TRANSACTIONS ON ROBOTICS
, 2008
"... Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dyna ..."
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Cited by 38 (4 self)
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Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any aprioriassignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, distributed multidestination potential fields are developed that are able to drive every agent to any available destination. Second, nearest neighbor coordination protocols are developed ensuring that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Furthermore, we show that our dynamic assignment algorithm will converge after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.
Configuration spaces and braid groups on graphs in robotics
, 1999
"... Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the construction and classification of configuration spaces for gr ..."
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Cited by 35 (3 self)
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Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the construction and classification of configuration spaces for graphs. Topological data associated to these spaces (e.g., dimension, braid groups) provide an effective measure of the complexity of the control problem. The spaces are themselves topologically interesting objects. We show that they are K(π1, 1) spaces whose homological dimension is bounded by the number of essential vertices. Hence, the braid groups are torsionfree.
Vehicle Motion Planning Using Stream Functions
 in IEEE International Conference on Robotics and Automation
, 2003
"... Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a localminima free method for producing potentialfield based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraftl ..."
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Cited by 32 (3 self)
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Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a localminima free method for producing potentialfield based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraftlike vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed.
Finding topology in a factory: configuration spaces
 Amer. Math. Monthly
, 2002
"... It is perhaps not universally acknowledged that an outstanding place to find interesting topological objects is within the walls of an automated warehouse or factory. The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the ..."
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Cited by 31 (4 self)
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It is perhaps not universally acknowledged that an outstanding place to find interesting topological objects is within the walls of an automated warehouse or factory. The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the first author, in his thesis [1], discovered these spaces after working with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow on problems about random walks on graphs [2]. The second author discovered these same spaces while collaborating with D. Koditschek in the Artificial Intelligence Lab at the University of Michigan; see [7] and [8]. Sections 1 and 2 give some motivations arising from robotics, as well as a little background on configuration spaces. For the remainder of the paper we focus on a fascinating class of topological spaces related to motionplanning on graphs. 1. Robotics and topological motion planning Consider an automated factory equipped with a cadre of Automated Guided