This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the close...

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...

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We are interested in using low degree-of-freedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form- or force-closure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof -freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight.

We address the motion planning for 'xtureless" material-handling with multiple manipulators on nonholonomic carts. The mobile manipulators possess the ability to manipulate and transport objects while holding them in a stable grasp. We present a general approach that allows generation of optimal trajectories and actuator inputs for any given maneuver. Constraints such as limitations on the turning radii of the mobile manipulators or bounds on their separation can be easily incorporated into the planning scheme. Numerical solutions for several maneuvers including abrupt turns, parallel parking in cluttered environments and changes in formation are computed. Finally, we present escperimental results with two mobile manipulators.

This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal control problem and describe a general framework and an algorithm to obtain numerical solutions to this problem. This work employs optimal control techniques to study the optimality of gaits and issues involving gait transitions. The general framework provided in this paper can easily be applied to other examples of biological and robotic locomotion. KEY WORDS---optimal control, robotic locomotion, geometric mechanics, locomotive gaits 1.

This paper presents a direct method for computing the time optimal trajectory for a robot among stationary and moving obstacles, subject to robot's dynamics and actuator constraints. The motion planning problem is first formulated as an optimization problem, and then solved numerically using a gradient descent. The initial guess for the optimization is generated using a method based on the concept of Velocity Obstacles. The method is demonstrated for a 2-DOF planar manipulator moving in static and dynamic environments. 1. Introduction Motion planning is central to the operation of autonomous robots. It concerns the generation of a trajectory from start to goal that satisfies objectives, such as minimizing path distance or motion time, while avoiding obstacles in the environment and satisfying the robot mechanics (kinematics and dynamics). We distinguish between planning and control in that the former generates a nominal trajectory, whereas the latter tracks that trajectory. Robot mot...

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.

this paper are in finding paths for nonholonomic systems. These systems are characterized by having nonintegrable constraints on the state velocities which do not restrict the reachable configuration space. There is a classical result from nonlinear control theory [6] which can be used to prove that such systems are completely controllable, implying that a feasible path exists between any two points in free space. This result, however, does not have a constructive proof. The problem we consider in this paper is the construction of a feasible path between the start and goal states. We transform the path-planning problem with constraints on the velocities into the dual control problem with fewer control inputs than degrees of freedom. Some early work by Murray and Sastry (see [5]) used sinusoidal inputs at varying frequencies to plan paths for systems in a special chained canonical form. More recently, it has been shown by Monaco and Normand-Cyrot [4] that piecewise constant controls may be used for nonholonomic path planning. The system that we use as our example was originally examined in [1]. It has three control inputs and can be shown to be completely controllable. In addition, the system can be transformed into a specific class of nilpotent systems called chained form systems. Using these chained form coordinates, We apply the multi-rate control scheme to the example system. We also present some simulation results, comparing the multi-rate and sinusoidal algorithms on three different trajectories. Our findings are that the paths generated by the multi-rate control scheme are shorter and more direct than the paths generated by the sinusoidal path-planning algorithm.

Nonholonomic constraints in robotic systems are the source of some di#culties in planning and control; however, they also introduce interesting properties that can be practically exploited. In this paper we consider the design of a robot hand that achieves dexterity #i.e., the ability to arbitrarily locate and reorient manipulated objects# through rolling. Some interesting issues arising in planning and controlling motions of such device are considered, including exact planning for a spherical object and approximate planning for general objects. An experimental prototype of a three#plus#one d.o.f. hand achieving dexterous manipulation capabilities is described along with experimental results from manipulation. 1 Introduction Dexterous hands, i.e. cooperating multilimb robots with the capability of manipulating an object so as to arbitrarily steer its con#guration in space, have attracted muchinterest in the robotics literature. However, the high degree of sophistication in their mech...