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82
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
 IEEE Transactions on Automatic Control
, 2000
"... In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimensi ..."
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Cited by 94 (26 self)
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In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space. Local controllability properties of these systems are characterized, and two algebraic tests are derived in terms of the symmetric product and the Lie bracket of the input vector fields. Perturbation theory is applied to compute approximate solutions for the system under smallamplitude forcing; inphase signals play a crucial role in achieving motion along symmetric product directions. Motion control algorithms are then designed to solve problems of pointtopoint reconfiguration, static interpolation and exponential stabilization. We illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies, satellites and underwater vehicles.
WMR Control Via Dynamic Feedback Linearization: Design, Implementation, and Experimental Validation
, 2002
"... The subject of this paper is the motion control problem of wheeled mobile robots (WMRs) in environments without obstacles. With reference to the popular unicycle kinematics, it is shown that dynamic feedback linearization is an efficient design tool leading to a solution simultaneously valid for bot ..."
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Cited by 75 (4 self)
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The subject of this paper is the motion control problem of wheeled mobile robots (WMRs) in environments without obstacles. With reference to the popular unicycle kinematics, it is shown that dynamic feedback linearization is an efficient design tool leading to a solution simultaneously valid for both trajectory tracking and setpoint regulation problems. The implementation of this approach on the laboratory prototype SuperMARIO, a twowheel differentially driven mobile robot, is described in detail. To assess the quality of the proposed controller, we compare its performance with that of several existing control techniques in a number of experiments. The obtained results provide useful guidelines for WMR control designers.
Trajectory Generation for the NTrailer Problem Using Goursat Normal Form
, 1995
"... In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the p ..."
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Cited by 73 (10 self)
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In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the problem of rbxing a mobile robot WMI R trailers. We present an algorithm for finding a family of ~WIS~~~OM whicb will convert the system of rolling constraints on the wheels of the robot with n traiten into the GoaFapt canonical form..nRo of these transformations are studied in detail. The Gomt normal form for exterior diffemtial systems is dual to the socalled chainedform for vector fields that bas been studied previously. Consequently, we are able to give the state feedback law aad change o € e00rdinaW tovert the Ntrai4r system id0 chained form. Tllree metbods for for chainedform systems using shrosoidg and polynomiPls aa inputs are presented. The motion prpnnhag strategy Is therefore to the Ntrailer system into Gonrsat form, use this to lind the cboinedform coordinates, plan a path for the corresponding cimkdform system, and then transform the resalting traje.ctory back into the original coordinates. Simulations and h.ames of mode animations of the Ntnder system for parallel parking and backing into a loading dock using this strategy are included.
Nonholonomic Navigation and Control of Cooperating Mobile Manipulators
 IEEE Transactions on Robotics and Automation
, 2002
"... This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions (DILFs) and a novel extension of the navigation function metho ..."
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Cited by 72 (20 self)
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This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions (DILFs) and a novel extension of the navigation function method to account for nonpoint articulated robots. The Dipolar Inverse Lyapunov Functions introduced are appropriate for nonholonomic control and offer superior performance characteristics compared to existing tools. The new potential field technique uses diffeomorphic transformations and exploits the resulting pointworld topology. The combined approach is applied to the problem of handling deformable material by multiple nonholonomic mobile manipulators in obstacle environment to yield a centralized coordinating control law. Simulation results verify asymptotic convergence of the robots, obstacle avoidance, boundedness of object deformations and singularity avoidance for the manipulators. Index TermsNonholonomic motion planning, cooperative mobile manipulators, potential fields, Inverse Lyapunov Functions.
Control of Underactuated Mechanical Systems with two Degrees of Freedom and Symmetry
"... In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained ..."
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Cited by 66 (10 self)
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In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained from the Lagrangian of the system that transforms the system into a partially linear cascade nonlinear system that is strict feedback. The nonlinear part of this system is nona#ne in control and this highly complicates control design for the system. We provide conditions under which this nonlinear subsystem can be globally stabilized and give globally stabilizing control laws for it. The strict feedback structure of the system in new coordinates allows us to obtain a globally stabilizing control law for the composite system using standard backstepping. We apply our result to global asymptotic stabilization of the Acrobot.
The Geometric Mechanics of Undulatory Robotic Locomotion
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion pro ..."
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Cited by 66 (14 self)
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This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have a natural geometric interpretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "Snakeboard" and a multisegmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.
LogicBased Switching Algorithms in Control
, 1998
"... This thesis deals with the use of logicbased switching in the control of imprecisely modeled nonlinear systems. Each control system considered consists of a continuoustime dynamical process to be controlled, a family of candidate controllers, and an eventdriven switching logic. The need for switc ..."
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Cited by 45 (23 self)
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This thesis deals with the use of logicbased switching in the control of imprecisely modeled nonlinear systems. Each control system considered consists of a continuoustime dynamical process to be controlled, a family of candidate controllers, and an eventdriven switching logic. The need for switching arises when no single candidate controller is capable, by itself, of guaranteeing good performance when connected with a poorly modeled process. In this thesis we develop provably correct switching strategies capable of determining in realtime which candidate controller should be put in feedback with a process so as to achieve a desired closedloop performance. The resulting closedloop systems are hybrid in the sense that in each case, continuous dynamics interact with eventdriven logic. In the process of designing these switching algorithms, we develop several tools for the analysis and synthesis o...
Practical stabilization of driftless systems on Lie groups: the transverse function approach
 IEEE Trans. on Automatic Control,48,1496
, 2003
"... Abstract—A general control design approach for the stabilization of controllable driftless nonlinear systems on finite dimensional Lie groups is presented. The approach is based on the concept of bounded transverse functions, the existence of which is equivalent to the system’s controllability. Its ..."
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Cited by 38 (12 self)
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Abstract—A general control design approach for the stabilization of controllable driftless nonlinear systems on finite dimensional Lie groups is presented. The approach is based on the concept of bounded transverse functions, the existence of which is equivalent to the system’s controllability. Its outcome is the practical stabilization of any trajectory, i.e., not necessarily a solution of the control system, in the state–space. The possibility of applying the approach to an arbitrary controllable smooth driftless system follows in turn from the fact that any controllable homogeneous approximation of this system can be lifted (via a dynamic extension) to a system on a Lie group. Illustrative examples are given. Index Terms—Feedback law, Lie groups, nonlinear systems, stabilization.
Design of homogeneous timevarying stabilizing control laws for driftless controllable systems via oscillatory approximation of Lie brackets in closedloop
, 1999
"... A constructive method for timevarying stabilization of smooth driftless controllable systems is developed. It provides timevarying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closedloop system globally exponentially asymptotically stabl ..."
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Cited by 35 (6 self)
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A constructive method for timevarying stabilization of smooth driftless controllable systems is developed. It provides timevarying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closedloop system globally exponentially asymptotically stable if the control system is homogeneous with respect to a family of dilations and, using local homogeneous approximation of control systems, locally exponentially asymptotically stable otherwise. The method uses some known algorithms that construct oscillatory control inputs to approximate motion in the direction of iterated Lie brackets that we adapt to the closedloop context.
Stabilization of Nonholonomic Integrators via LogicBased Switching
, 1996
"... This paper demonstrates how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic. Results concerning asymptotic stability and exponentially fast convergence to the origin are derived. The methodology used seems to be generalizable to a larger class of con ..."
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Cited by 35 (4 self)
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This paper demonstrates how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic. Results concerning asymptotic stability and exponentially fast convergence to the origin are derived. The methodology used seems to be generalizable to a larger class of control problems related to nonholonomic systems.