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 multi-segmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.

This thesis deals with the use of logic-based switching in the control of imprecisely modeled nonlinear systems. Each control system considered consists of a continuous-time dynamical process to be controlled, a family of candidate controllers, and an event-driven 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 real-time which candidate controller should be put in feedback with a process so as to achieve a desired closed-loop performance. The resulting closed-loop systems are hybrid in the sense that in each case, continuous dynamics interact with event-driven logic. In the process of designing these switching algorithms, we develop several tools for the analysis and synthesis o...

This paper presents the first motion planning methodology applicable to articulated, non-point 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 non-point 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 Terms---Nonholonomic motion planning, cooperative mobile manipulators, potential fields, Inverse Lyapunov Functions.

A constructive method for time-varying stabilization of smooth driftless controllable systems is developed. It provides time-varying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closed-loop 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 closed-loop context.

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.

: 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 multi-segmented 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...

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 two-wheel 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.

. In this paper we study the stabilization problem for control systems defined on SE(3) (the special Euclidean group of rigid-body 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 coordinate-free 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...

This paper presents a motion planner and nonholonomic controller for a mobile robot, with global collision avoidance and convergence properties. This closed loop approach combines appropriately designed (dipolar) potential fields with discontinuous feedback and is suitable for real time implementation. It makes use of a novel kind of Lyapunov functions which are useful for nonholonomic navigation. The obstacle avoidance and global asymptotic stability properties of the closed loop system are verified through computer simulations.

This paper considers the task of stabilization for underactuated mechanical systems via highamplitude, high-frequency actuation. Using higher order averaging techniques, we extend previous work to the case where symmetric products of order higher than one are necessary for controllability. We rst introduce a second order averaged mechanical system model that incorporates higher order terms. Using this result, we can obtain trajectory tracking by feeding back an error signal that is kept constant over whole periods of the oscillatory actuation. Simulations demonstrate the method. 1