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55
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 60 (9 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.
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 57 (15 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.
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 40 (11 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.
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 39 (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...
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 34 (1 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.
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 27 (3 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 26 (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.
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 22 (7 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.
Geometric Perspectives on the Mechanics and Control of Robotic Locomotion
 In Proc. International Symposium on Robotics Research
, 1995
"... : This paper uses geometric methods to study basic problems in locomotion. We consider in detail the case of "undulatory locomotion," which is generated by a coupling of internal shape changes to external nonholonomic constraints. Such locomotion problems can be modeled as a connection on ..."
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Cited by 19 (4 self)
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: This paper uses geometric methods to study basic problems in locomotion. We consider in detail the case of "undulatory locomotion," which is generated by a coupling of internal shape changes to external nonholonomic constraints. Such locomotion problems can be modeled as a connection on a principal fiber bundle. The properties of connections lead to simplified results for both the dynamics and controllability of locomotion systems. We demonstrate the utility of this approach on a novel "Snakeboard" and a multisegmented serpentine robot which is modeled after Hirose's ACM. 1 Introduction and Motivation A large body of research has developed in the area of robotic locomotion, since mobility is an important capability for autonomous systems. Most mobile robots are wheeled vehicles, since wheels provide the simplest means for mobility. The assumption that these wheels do not slip provides nonholonomic kinematic constraints on a vehicle's motion, and these kinematic nonholonomic system...
Proportional Derivative (PD) Control On The Euclidean Group
 In European Control Conference
, 1995
"... . In this paper we study the stabilization problem for control systems defined on SE(3) (the special Euclidean group of rigidbody motions) and its subgroups. Assuming one actuator is available for each degree of freedom, we exploit geometric properties of Lie groups (and corresponding Lie algebras) ..."
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Cited by 14 (2 self)
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. In this paper we study the stabilization problem for control systems defined on SE(3) (the special Euclidean group of rigidbody motions) and its subgroups. Assuming one actuator is available for each degree of freedom, we exploit geometric properties of Lie groups (and corresponding Lie algebras) to generalize the classical proportional derivative (PD) control in a coordinatefree way. For the SO(3) case, the compactness of the group gives rise to a natural metric structure and to a natural choice of preferred control direction: an optimal (in the sense of geodesic) solution is given to the attitude control problem. In the SE(3) case, no natural metric is uniquely defined, so that more freedom is left in the control design. Different formulations of PD feedback can be adopted by extending the SO(3) approach to the whole of SE(3) or by breaking the problem into a control problem on SO(3) \Theta R 3 . For the simple SE(2) case, simulations are reported to illustrate the behavior of...