Amit Ailon

An observer-based set-point controller for robot manipulators with flexible joints

We present a globally asymptotically stable controller for point-to-point regulation of robot manipulators with flexible joints that uses only position measurement on the motor side. Existing asymptotically stable schemes for the set point regulation problem without velocity measurement address only the rigid robot case. Furthermore, these solutions ensure only local stability provided some bounds on the dynamic part of the robot model are known. Also, they require the injection of high gains into the loop to enlarge the equilibrium domain of attraction. In contrast, our solution is global, applies for robots with flexible joints and assumes only that the gravity forces are known. The underlying rationale of the design is to ‘shape’ the potential energy of the closed loop system so that it has an absolute minimum at the desired equilibrium, and add the required dampingto achieve asymptotic stability. This is attained by adding a (linear) observer that converges to the position required to compensate the gravity forces and injects the damping, and a ‘spring-like’ effect between the observer and the robot that ‘pulls’ the robot to the desired target. This approach to observer-based controller design differs from the classical certainly equivalent approach and effectively exploits the dynamic properties of the physical system.

Brief On controllability and trajectory tracking of a kinematic vehicle model

This paper presents some further results concerning the issues of controllability and trajectory tracking regarding a front-wheel drive vehicle kinematic model. A simple procedure for computing an open-loop control strategy that transfers the system between given initial and final states, is presented. In particular, the input function is computed by means of a set of linear algebraic equations. The resulting motion planning procedure allows us to present a control scheme for solving the trajectory (a time-parameterized reference signal) tracking problem. Various applications of the approach in forward and backward motions are considered, and simulation results are presented.

A simple velocity-free controller for attitude regulation of a spacecraft with delayed feedback

In this note, we consider the application of a velocity-free controller for attitude regulation of a rigid spacecraft with gas jet actuators when the effects of time-delays in the feedback loop are taken into consideration. Simple sufficient conditions for exponential stability are presented. Some structural properties of the resulting closed-loop system are studied, and relevant design tools are demonstrated.

Simple Tracking Controllers for Autonomous VTOL Aircraft With Bounded Inputs

This note presents simple controllers for achieving asymptotic trajectory (set-point and time-varying) tracking under the conditions of restricted input in vertical takeoff and landing aircraft. Unlike previous studies that apply nonlinear combination of saturated functions for stabilizing the closed-loop system, the proposed controllers are based on smooth functions that can easily be implemented in real time applications.

On the existence of time-optimal control of mechanical manipulators

This paper is concerned with the problem of the existence and structure of time-optimal control for models derived from Lagrange equations of motion of mechanical systems involving links. The condition which ensures the existence of time-optimal control is demonstrated. The study conducted in this paper involves a highly nonlinear mathematical model of a two-degree-of-freedom mechanical system. However, the procedure and the results presented in this paper can be extended to mechanical systems with any finite number of degrees of freedom.

Control Strategies for Driving a Group of Nonholonomic Kinematic Mobile Robots in Formation Along a Time-Parameterized Path

This paper proposes control schemes for a group of nonholonomic kinematic mobile robots for maintaining a desired formation along a time-parameterized path. The control approach is based in particular on the flatness property and the concept of virtual vehicles. The control objective is twofold: to maintain the formation structure during motion along a desired geometric path, and to follow a timing law that dominates the rate of advancement of the group and the arrival times to assigned sites. This paper suggests, in particular, control strategies for convoy-like vehicles and for rigid formations. The leading vehicle governs the overall group motion. However, each member of the group can independently split or merge and maneuver to avoid collision (assuming that the relevant data are available by communication/sensing means) during the group motion.

Mobile robot characterized by dynamic and kinematic equations and actuator dynamics: Trajectory tracking and related application

This paper establishes control strategies for wheeled mobile robots which are subjected to nonholonomic constraints. The mobile robot model includes the kinematic and dynamic equations of motion and the actuator dynamics. Using the notion of virtual vehicle and the concept of flatness, and applying the backstepping methodology the paper proposes control schemes for trajectory tracking for the considered augmented model of the mobile robot. The resulting controller ensures exponential convergence to a desired trajectory. Applications of the tracking controller for convoy-like vehicles governed by the augmented models are considered as well. Simulation results and lab experiments are demonstrated.

Output controllers based on iterative schemes for set-point regulation of uncertain flexible-joint robot models

This paper considers the set-point regulation problem of a flexible-joint robot with unknown parameters where only position measurements are available. The proposed iterative schemes guarantee that every system response converges to an arbitrarily small neighborhood of the equilibrium point. An essential tool in the present approach is the contraction mapping theorem.

Semi-global stabilization of discrete-time systems with bounded inputs using a periodic controller

We show that semi-global stabilization is achieved for linear discrete-time systems with bounded controls. The proposed scheme is a linear periodic controller and is applicable to systems having open-loop eigenvalues in the closed unit disc.

Stability analysis of a rigid robot with output-based controller and time delay ☆

This study considers the problem of stabilizing a rigid robot with an output-based controller and time-delayed input functions applied to the robot joints. We establish sufficient conditions for asymptotic stability of the system under consideration. These conditions are based on well-defined relationships between the magnitude of the controller gains and the time delay factor.