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82
RealTime Motion Planning For Agile Autonomous Vehicles
 AIAA JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS
, 2000
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Feedback Control of Dynamic Bipedal Robot Locomotion
, 2007
"... The objective of this book is to present systematic methods for achieving stable, agile and efficient locomotion in bipedal robots. The fundamental principles presented here can be used to improve the control of existing robots and provide guidelines for improving the mechanical design of future rob ..."
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Cited by 130 (24 self)
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The objective of this book is to present systematic methods for achieving stable, agile and efficient locomotion in bipedal robots. The fundamental principles presented here can be used to improve the control of existing robots and provide guidelines for improving the mechanical design of future robots. The book also contributes to the emerging control theory of hybrid systems. Models of legged machines are fundamentally hybrid in nature, with phases modeled by ordinary differential equations interleaved with discrete transitions and reset maps. Stable walking and running correspond to the design of asymptotically stable periodic orbits in these hybrid systems and not equilibrium points. Past work has emphasized quasistatic stability criteria that are limited to flatfooted walking. This book represents a concerted effort to understand truly dynamic locomotion in planar bipedal robots, from both theoretical and practical points of view. The emphasis on sound theory becomes evident as early as Chapter 3 on modeling, where the class of robots under consideration is described by lists of
Reactive Path Deformation for Nonholonomic Mobile Robots
, 2004
"... This paper presents a novel and generic approach of path optimization for nonholonomic systems. The approach is applied to the problem of reactive navigation for nonholonomic mobile robots in highly cluttered environments. A collisionfree initial path being given for a robot, obstacles detected whi ..."
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Cited by 60 (4 self)
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This paper presents a novel and generic approach of path optimization for nonholonomic systems. The approach is applied to the problem of reactive navigation for nonholonomic mobile robots in highly cluttered environments. A collisionfree initial path being given for a robot, obstacles detected while following this path can make it in collision. The current path is iteratively deformed in order to ge away from obtacles and satisfy the nonholonomic constraints. The core idea of the approach is to perturb the input functions of the system along the current path in order to modify this path, making an optimization criterion decrease.
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
CollisionFree Trajectory Planning for a 3DOF Robot with a Passive Joint
 International Journal of Robotics Research
, 2000
"... This paper studies motion planning from one zero velocity state to another for a threejoint robot in a horizontal plane with a passive revolute third joint. Such a robot is smalltime locally controllable on an open subset of its zero velocity section, allowing it to follow any path in this subset ..."
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Cited by 29 (5 self)
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This paper studies motion planning from one zero velocity state to another for a threejoint robot in a horizontal plane with a passive revolute third joint. Such a robot is smalltime locally controllable on an open subset of its zero velocity section, allowing it to follow any path in this subset arbitrarily closely. However, some paths are "preferred" by the dynamics of the manipulator in that they can be followed at higher speeds. In this paper we describe a computationally efficient trajectory planner which finds fast collisionfree trajectories among obstacles. We are able to decouple the problem of planning feasible trajectories in the robot's sixdimensional state space into the computationally simpler problems of planning paths in the threedimensional configuration space and time scaling the paths according to the manipulator dynamics. This decoupling is made possible by the existence of velocity directions, fixed in the passive link frame, which can be executed at arbitrary ...
Loworder controllability and kinematic reductions for affine connection control systems
 SIAM Journal on Control and Optimization
"... Abstract. Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynami ..."
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Cited by 22 (6 self)
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Abstract. Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynamic (i.e., have forces as inputs) and those which are kinematic (i.e., have velocities as inputs). Interestingly and surprisingly, these two subjects are characterised and linked by a certain intrinsic vectorvalued quadratic form that can be associated to an affine connection control system.
Nonlinear control of mechanical systems with one degree of underactuation
 IN PROC. OF THE IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2004
"... Numerous robotic tasks associated with underactuation have been studied in the literature. For a large number of these in the plane, the mechanical models have a cyclic variable, the cyclic variable is unactuated, and all shape variables are independently actuated. This paper formulates and solves ..."
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Cited by 21 (5 self)
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Numerous robotic tasks associated with underactuation have been studied in the literature. For a large number of these in the plane, the mechanical models have a cyclic variable, the cyclic variable is unactuated, and all shape variables are independently actuated. This paper formulates and solves two control problems for this class of models. If the generalized momentum conjugate to the cyclic variable is not conserved, conditions are found for the existence of a set of outputs that yields a system with a onedimensional exponentially stable zero dynamics — i.e. an exponentially minimumphase system — along with a dynamic extension that renders the system locally inputoutput decouplable. If the generalized momentum conjugate to the cyclic variable is conserved, a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics, along with a dynamic extension that renders the system feedback linearizable. A common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components. The function arises by partially integrating the conjugate momentum. The results are illustrated on two balancing tasks and on a ballistic flip motion.
Controllable Kinematic Reductions for Mechanical Systems: Concepts, Computational Tools, and Examples
, 2002
"... This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model them as a#ne connection control systems. For these systems, a kinematic reducti ..."
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Cited by 19 (4 self)
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This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model them as a#ne connection control systems. For these systems, a kinematic reduction is a driftless control system whose controlled trajectories are also solutions to the full dynamic model under appropriate controls. We present a comprehensive treatment of local controllability properties of mechanical systems and their kinematic reductions. Remarkably, a number of interesting reduction and controllability conditions can be characterized in terms of a certain vectorvalued quadratic form. We conclude with a catalog of example systems and their kinematic reductions.
Simple Mechanical Control Systems With Constraints And Symmetry
, 2002
"... We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the LeviCivita and the nonholonomic affine connect ..."
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Cited by 18 (5 self)
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We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the LeviCivita and the nonholonomic affine connections, along with the symmetric product, in the presence of symmetries and nonholonomic constraints. We note that there are naturally two kinds of connections to be considered here, affine and principal connections, leading to what we term a "connection within a connection". These results are then used to describe controllability tests that are specialized to simple, underactuated mechanical systems on principal fiber bundles, including the notion of fiber configuration controllability. We present examples of the use of these tools in studying the planar rigid body with a variable direction (vectored) thruster and the snakeboard robot.