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This paper concerns a simple extension of Lord Kelvin's observation that energy decays in a dissipative mechanical system. The global limit behavior ofsuch systems can be made essentially equivalent to that of much simpler gradient systems by the introduction of a "navigationfunction" in the role of an artificial field. This recourse to the mechanical system's natural motion helps transform the open-ended problem of autonomous machine design into the more structured problem of finding an appropriate "cost function" in the many situations that the goal may be encoded as a setpoint problem with configuration constraints. This paper offers a unified exposition of some recent results [13, 12, 15] heretofore scattered throughout a more mathematically oriented literature that strengthen our original suggestion [8, 9] concerning the utility o...
Earlier results of this author and others demonstrate that a broad range of robotic tasks can be commanded through relatively simple feedback controllers with a guarantee of global asymptotic stability. A weakness of such methods is the requirement that exact values of all dynamical parameters be available, since they are used to cancel the disturbance torques introduced by gravity. An adaptive strategy is reported here which guarantees stability and global boundedness of a natural controller in the absence of à priori information regarding dynamical parameters. The present results, however, are not yet satisfactory since they cannot assure convergence to the correct spatial position.
Strict Lyapunov functions are constructed for a class of nonlinear feedback compensated mechanical systems, requiring no à priori information concerning the initial conditions of the closed-looped system. These Lyapunov functions may be used to design a stable adaptive version of the "computed-torque" algorithm for tracking a reference trajectory. A particular Lyapunov function is then generalized to permit an adaptive version of control scheme forced by reference dynamics rather than reference trajectory.
This paper presents two setpoint regulation problems that may be distinguished from the traditional preview of feedback design by the a priori impossibility of building a smooth bounded controller whose closed loop yields asymptotic stability while preserving configuration constraints. An appeal to the theoretical ideas introduced in [13] yields a solution to each of these problems in the form of a navigation function thatserves as an instance of the natural control philosophy. That is to say, the intrinsic dynamics of the mechanical system, when properly "programmed" are capable of "solving" what have often been cast as planning problems. The resulting closed loop behavior demonstrates a kind of autonomy in that the goal is achieved with probability one and with no further intervention on the part of a "higher level planner."
This paper reviews the theory of navigation functions and the attendant use of natural control techniques with emphasis upon applications to mobile autonomous robots. Results to date will be discussed in the context of a larger program of research that seeks effective parameterizations of uncertainty in robot navigation problems. Constructive solutions to particular cases of mobile robot navigation problems with complete certainty are provided as well.
This paper introduces a class of linearizing coordinate transformations for mechanical systems whose moment of inertia matrix has a square root which is a jacobian. The transformations, when they exist, define a local isometry from joint space to euclidean space, hence, may afford further insight into the transient behavior of robot motion. It remains to be seen whether any appreciably large class of robots admit such linearizing isometries.
This paper describes some initial steps toward the development of more natural control strategies for free motion of robot arms. The standard lumped parameter dynamical model of an open kinematic chain is shown to be stabilizable by linear feedback, after nonlinear gravitational terms have been cancelled. A new control algorithm is proposed and is shown to drive robot joint positions and velocities asymptotically toward arbitrary time-varying reference trajectories.
A program of research in robotics that seeks to encode abstract tasks in a form that simultaneously affords a control scheme for the torque-actuated dynamical systems, as well as a proof that the resulting closed-loop behavior will correctly achieve the desired goals, is reviewed. Two different behaviors that require dexterity and might plausibly connote 'intelligence' - navigating in a cluttered environment and juggling a number of otherwise freely falling objects - are examined with regard to similarities in problem representation, method of solution, and causes of success. The central theme concerns the virtue of global stability mechanisms. At the planning level they lend autonomy, that is, freedom from dependence upon some 'higher' intelligence. They encourage the design of canonical procedures for model problems, which may then b...
The introduction of "error coordinates" and a "tracking potential" on the rotations affords a global nonlinear version of inverse dynamics for attitude tracking. The resulting algorithm produces "almost global" asymptotically exact tracking: this convergence behavior is as strong as the topology of the phase space can allow. A new family of strict global Lyapunov functions for mechanical systems is applied to achieve an adaptive version of the inverse dynamics algorithm in the case that the inertial parameters of the rigid body are not known a priori. The resulting closed loop adaptive system is shown to be stable, and the rigid body phase errors are shown to converge to the limit trajectories of the non-adaptive algorithm.
Assembly problems require that a robot with fewer actuated degrees of freedom manipulate an environment containing a greater number of unactuated degrees of freedom. From the perspective of control theory, these problems hold considerable interest because they are characterized by the presence of non-holonomic constraints that preclude the possibility of feedback stabilization. In this sense they necessitate the introduction of a hierarchical controller. This paper explores these issues in the simple instance when all of the pieces to be assembled are constrained to lie on a line. A hierarchical controller is devised for this problem and is shown to be correct: the closed loop system achieves any desired final assembly from all initial configurations that lie in its connected component in configuration space; the generated sequence of ...
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