Warren E. Dixon

Nonlinear coupling control laws for an underactuated overhead crane system

In this paper, we consider the regulation control problem for an underactuated overhead crane system. Motivated by recent passivity-based controllers for underactuated systems, we design several controllers that asymptotically regulate the planar gantry position and the payload angle. Specifically, utilizing LaSalles invariant set theorem, we first illustrate how a simple proportional-derivative (PD) controller can be utilized to asymptotically regulate the overhead crane system. Motivated by the desire to achieve improved transient performance, we then present two nonlinear controllers that increase the coupling between the planar gantry position and the payload angle. Experimental results are provided to illustrate the improved performance of the nonlinear controllers over the simple PD controller.

Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction

Modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. This interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical ramifications. If the friction effects in the system can be accurately modeled, there is an improved potential to design controllers that can cancel the effects; whereas, excessive steady-state tracking errors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. A tracking controller is developed in this paper for a general Euler-Lagrange system that contains a new continuously differentiable friction model with uncertain nonlinear parameterizable terms. To achieve the semi-global asymptotic tracking result, a recently developed integral feedback compensation strategy is used to identify the friction effects online, assuming exact model knowledge of the remaining dynamics. A Lyapunov-based stability analysis is provided to conclude the tracking and friction identification results. Experimental results illustrate the tracking and friction identification performance of the developed controller.

A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems

An online adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem for continuous-time uncertain nonlinear systems. A novel actor-critic-identifier (ACI) is proposed to approximate the Hamilton-Jacobi-Bellman equation using three neural network (NN) structures-actor and critic NNs approximate the optimal control and the optimal value function, respectively, and a robust dynamic neural network identifier asymptotically approximates the uncertain system dynamics. An advantage of using the ACI architecture is that learning by the actor, critic, and identifier is continuous and simultaneous, without requiring knowledge of system drift dynamics. Convergence of the algorithm is analyzed using Lyapunov-based adaptive control methods. A persistence of excitation condition is required to guarantee exponential convergence to a bounded region in the neighborhood of the optimal control and uniformly ultimately bounded (UUB) stability of the closed-loop system. Simulation results demonstrate the performance of the actor-critic-identifier method for approximate optimal control.

Asymptotic Tracking for Systems With Structured and Unstructured Uncertainties

The control of systems with uncertain nonlinear dynamics has been a decades-long mainstream area of focus. The general trend for previous control strategies developed for uncertain nonlinear systems is that the more unstructured the system uncertainty, the more control effort (i.e., high gain or high-frequency feedback) is required to cope with the uncertainty, and the resulting stability and performance of the system is diminished (e.g., uniformly ultimately bounded stability). This brief illustrates how the amalgamation of an adaptive model-based feedforward term (for linearly parameterized uncertainty) with a robust integral of the sign of the error (RISE) feedback term (for additive bounded disturbances) can be used to yield an asymptotic tracking result for Euler-Lagrange systems that have mixed unstructured and structured uncertainty. Experimental results are provided that illustrate a reduced root-mean-squared tracking error with reduced control effort.

Homography-based visual servo regulation of mobile robots

A monocular camera-based vision system attached to a mobile robot (i.e., the camera-in-hand configuration) is considered in this paper. By comparing corresponding target points of an object from two different camera images, geometric relationships are exploited to derive a transformation that relates the actual position and orientation of the mobile robot to a reference position and orientation. This transformation is used to synthesize a rotation and translation error system from the current position and orientation to the fixed reference position and orientation. Lyapunov-based techniques are used to construct an adaptive estimate to compensate for a constant, unmeasurable depth parameter, and to prove asymptotic regulation of the mobile robot. The contribution of this paper is that Lyapunov techniques are exploited to craft an adaptive controller that enables mobile robot position and orientation regulation despite the lack of an object model and the lack of depth information. Experimental results are provided to illustrate the performance of the controller.

Asymptotic Tracking for Uncertain Dynamic Systems Via a Multilayer Neural Network Feedforward and RISE Feedback Control Structure

The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UUB) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global asymptotic tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates.

Adaptive Regulation of Amplitude Limited Robot Manipulators With Uncertain Kinematics and Dynamics

Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this note, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semiglobal asymptotic regulation of the task-space setpoint error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure actuator constraints are not breached by calculating the maximum required torque a priori

Range identification for perspective vision systems

In this note, a new observer is developed to determine range information (and, hence, the three-dimensional (3-D) coordinates) of an object feature moving with affine motion dynamics (or the more general Ricatti motion dynamics) with known motion parameters. The unmeasurable range information is determined from a single camera provided an observability condition is satisfied that has physical significance. To develop the observer, the perspective system is expressed in terms of the nonlinear feature dynamics. The structure of the proposed observer is inspired by recent disturbance observer results. The proposed technique facilitates a Lyapunov-based analysis that is less complex than the sliding-mode based analysis derived for recent observer designs. The analysis demonstrates that the 3-D task-space coordinates of the feature point can be asymptotically identified. Simulation results are provided that illustrate the performance of the observer in the presence of noise.

A new continuously differentiable friction model for control systems design

For high-performance engineering systems, model-based controllers are typically required to accommodate for the system nonlinearities. Unfortunately, developing accurate models for friction has been historically challenging. Typical models are either discontinuous and many other models are only piecewise continuous. Motivated by the fact that discontinuous and piecewise continuous friction models are problematic for the development of high-performance continuous controllers, a new model for friction is proposed in this paper. This simple continuously differentiable model represents a foundation that captures the major effects reported and discussed in friction modeling and experimentation. The proposed model is generic enough that other subtleties such as frictional anisotropy with sliding direction can be addressed by mathematically distorting this model without compromising the continuous differentiability

Fault detection for robot manipulators with parametric uncertainty: a prediction error based approach

In this paper, we introduce a new approach to fault detection for robot manipulators. The technique, which is based on the isolation of fault signatures via filtered torque prediction error estimates, does not require measurements or estimates of manipulator acceleration as is the case with some previously suggested methods. The method is formally demonstrated to be robust under uncertainty in the robot parameters. Furthermore, an adaptive version of the algorithm is introduced, and shown to both improve coverage and significantly reduce detection times. The effectiveness of the approach is demonstrated by experiments with a two-joint manipulator system.