Keith Dupree

Modular Adaptive Control of Uncertain Euler–Lagrange Systems With Additive Disturbances

A novel adaptive nonlinear control design is developed which achieves modularity between the controller and the adaptive update law. Modularity between the controller/update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and/or better tracking performance. For a general class of linear-in-the-parameters (LP) uncertain Euler-Lagrange systems subject to additive bounded non-LP disturbances, the developed controller uses a model-based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error (RISE) feedback term. Modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate. This generic form of the update law is used to develop a new closed-loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result.

Adaptive satellite attitude control in the presence of inertia and CMG gimbal friction uncertainties

A nonlinear adaptive attitude controller is designed in this paper that compensates for dynamic uncertainties in the spacecraft inertia matrix and unknown dynamic and static friction effects in the control moment gyroscope (CMG) gimbals. Attitude control torques are generated by means of a four single gimbal CMG pyramid cluster. The challenges to develop the adaptive controller are that the control input is multiplied by uncertainties due to dynamic friction effects and is embedded in a discontinuous nonlinearity due to static friction effects. A uniformly ultimately bounded result is proven via Lyapunov analysis for the case in which both static and dynamic gimbal friction is included in the dynamic model, and an extension is provided that illustrates how asymptotic tracking is achieved when only dynamic friction is present in the CMG model.

Asymptotic optimal control of uncertain nonlinear Euler-Lagrange systems

A sufficient condition to solve an optimal control problem is to solve the Hamilton-Jacobi-Bellman (HJB) equation. However, finding a value function that satisfies the HJB equation for a nonlinear system is challenging. For an optimal control problem when a cost function is provided a priori, previous efforts have utilized feedback linearization methods which assume exact model knowledge, or have developed neural network (NN) approximations of the HJB value function. The result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semi-global asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. An extension is included to illustrate how a NN can be combined with the previous results. Experimental results are given to demonstrate the proposed controllers.

Adaptive neural network satellite attitude control in the presence of inertia and CMG actuator uncertainties

A neural network-based adaptive attitude tracking controller is developed in this paper, which achieves attitude tracking in the presence of parametric uncertainty, nonlinear actuator disturbances, and unmodeled external disturbance torques, which do not satisfy the linear-in-the-parameters assumption (i.e., non-LP). The satellite control torques are produced by means of a cluster of control moment gyroscopes (CMGs), which have uncertain dynamic and static friction in the gimbals in addition to unknown electromechanical disturbances. Some challenges encountered in the control design are that the control input is premultiplied by a non-square, time-varying, nonlinear, uncertain matrix and is embedded in a discontinuous nonlinearity. Controller performance is proven via Lyapunov stability analysis.

Optimal control of uncertain nonlinear systems using RISE feedback

A Hamilton-Jacobi-Bellman optimization scheme is used along with a RISE feedback structure to minimize a quadratic performance index while the generalized coordinates of a nonlinear Euler-Lagrange system asymptotically track a desired time-varying trajectory despite general uncertainty in the dynamics, such as additive bounded disturbances and parametric uncertainty. Motivated by recent previous results that use a neural network structure to approximate the dynamics (i.e., the state space model is approximated with a residual function reconstruction error), the result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semi-global asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. Simulation results are included to demonstrate the performance of the developed controller.

Euclidean Calculation of Feature Points of a Rotating Satellite : A Daisy-Chaining Approach

Occlusion of feature points or feature points leaving the field of view (FOV) of a camera, is a significant practical problem that can lead to degraded performance or instability of visual servo control and vision-based estimation algorithms. In this paper, a new daisy chaining method is combined with image geometry to reconstruct the Euclidean coordinates of feature points even if they leave the FOV or become occluded. By assuming one known Euclidean distance between two feature points is available, homographic relationships and image geometry are used to determine the Euclidean coordinates of feature points in the field of view. The daisy chaining method is then used to relate the position and orientation of a plane defined by the feature points to other feature point planes that are rigidly connected. Through these relationships, the Euclidean coordinates of the original feature points can be tracked even as they leave the FOV. This objective is motivated by the desire to track the Euclidean coordinates of feature points on one face of a satellite as it continually rotates.

A Force Limiting Adaptive Controller for a Robotic System Undergoing a Noncontact-to-Contact Transition

The problem of prescribing, reducing, or controlling the interaction forces between a robot and the environment during a noncontact-to-contact transition is intriguing because large interaction forces can damage both the robot and/or the environment or lead to degraded performance or instabilities. In this paper, we consider a two-link planar robotic arm that transitions from free motion to contact with an unactuated mass-spring system. The objective is to control a robot from a noncontact initial condition to a desired (in-contact) position so that the mass-spring system is regulated to a desired compressed state. The feedback elements for the controller in this paper are contained inside hyperbolic tangent functions as a means to limit the impact forces resulting from large initial conditions as the robot transitions from a noncontact to contact state. The main challenge of this work is that the use of saturated feedback does not allow some coupling terms to be canceled in the stability analysis, resulting in the need to develop state-dependent upper bounds that reduce the stability to a semiglobal result. New control development, closed-loop error systems, and Lyapunov-based stability analysis arguments are used to conclude the result. It is interesting to note that only the position and velocity terms are required for the proposed controller (i.e., the controller does not depend on measuring the impact force and the acceleration terms). Experimental results that successfully demonstrate the control objective are provided.

Global Adaptive Lyapunov-Based Control of a Robot and Mass-Spring System Undergoing An Impact Collision

The control of dynamic systems that undergo an impact collision is both theoretically challenging and of practical importance. An appeal of studying systems that undergo an impact is that short-duration effects such as high stresses, rapid dissipation of energy, and fast acceleration and deceleration may be achieved from low-energy sources. However, colliding systems present a difficult control challenge because the equations of motion are different when the system status changes suddenly from a non-contact state to a contact state. In this paper an adaptive nonlinear controller is designed to regulate the states of two dynamic systems that collide. The academic example of a planar robot colliding with an unactuated spring-mass system is used to represent a broader class of such systems. The control objective is defined as the desire to command a robot to collide with an unactuated system and regulate the spring-mass to a desired compressed state while compensating for the unknown constant system parameters. Lyapunov-based methods are used to develop a continuous adaptive controller that yields global asymptotic regulation of the spring-mass and robot links. It is interesting to note that one controller is responsible for achieving the control objective when the robot is in free motion (i.e., decoupled from the mass-spring system), when the systems collide, and when the system dynamics are coupled

Lyapunov-based control of a robot and mass-spring system undergoing an impact collision

The control of a dynamic system with impact conditions is an interesting problem with practical importance. One difficulty in controlling systems subject to impact collisions is that the equations of motion are different when the system status changes suddenly from a non-contact state to a contact state. In this paper a nonlinear controller is designed to regulate the states of two dynamic systems that collide. The academic example of a planar robot colliding with an unactuated mass-spring system is used to represent a broader class of such systems. The control objective is to command a robot to collide with an unactuated mass-spring system and regulate the spring-mass to a desired compressed state. Lyapunov-based methods are used to develop a continuous controller that yields global asymptotic regulation of the spring-mass and robot links. Unlike some other results in literature, the developed continuous force controller does not depend on sensing the impact, measuring the impact force, or the measurement of other acceleration terms.

A new class of modular adaptive controllers, Part I: Systems with linear-in-the-parameters uncertainty

This paper presents a novel adaptive nonlinear control design which achieves modularity between the controller and the adaptive update law. Modularity between the controller/update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and/or better tracking performance. For a class of linear-in-the-parameters (LP) uncertain Euler-Lagrange systems subject to additive bounded non-LP disturbances, the result in this (Part I) paper is based on a controller that uses a model-based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error (RISE) feedback term. Modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate. This generic form of the update law is used to develop a new closed-loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result.