Albert A. Schy

Control of Elastic Robotic Systems by Nonlinear Inversion and Modal Damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Elastic Robot Control: Nonlinear Inversion and Linear Stabilization

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law Ud is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law us is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = ud + us.

Brief paper: Application of multiobjective optimization in aircraft control systems design

Multiobjective optimization techniques are applied in the design of an aircraft lateral control system. A large manned reentry vehicle and a fighter aircraft are considered. An algorithm suggested by Lins Proper Inequality Constraints method, is implemented in the numerical computation of Pareto-optimal solutions. Subsequently, a trade-off analysis of several Pareto-optimal solutions is conducted.

Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization

We present an approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a non-linear decoupling control law, ud, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, us, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u=ud+us.

Invertibility and robust nonlinear control of robotic systems

Based on the theory of invertibility and functional reproducibility in multivariable nonlinear systems, a unified framework for the trajectory control of robotic systems is presented. An inversion algorithm is used to derive a decoupling control law such that independent control of certain desired outputs is accomplished. For obtaining robustness in the control system under large variation of payloads, design of a servocompensator around the inner decoupled-loop using servomechanism theory is suggested. These results are applied for the trajectory control of a three degrees of freedom robot arm. For trajectory following two control laws, C¿ and CH, based on the choice of joint angles or coordinates of the end effector as the controlled outputs, respectively, are derived. It is seen that, whereas control C¿ has no singularity, certain singular surfaces arise where feedback elements of CH become infinity. Digital simulation results are presented to show the capability of the controls C¿ and CH.

Robust Trajectory Following Control of Robotic Systems

Using an inversion approach we derive a control law for trajectory following of robotic systems. A servocompensator is used around the inner decoupled loop for robustness to uncertainty in the system. These results are applied to trajectory control of a three-degrees-of-freedom robot arm and control laws Cθ and CH for joint angle and position trajectory following, respectively, are derived. Digital simulation results are presented to show the rapid trajectory following capability of the controller in spite of payload uncertainty.

Decomposition and State Variable Feedback Control of Elastic Robotic Systems

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. We present in this paper an approach to control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and, in addition, asymptotically decomposes the elastic dynamics into two subsystems. This allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results show that the combination of nonlinear decoupling and elastic stabilization permits rapid, accurate tracking of large joint angle commands with well damped elastic response, in spite of space vehicle motion and payload uncertainty.

Multicriteria Optimization Methods for Design of Aircraft Control Systems

In the design of airplane control systems, many disparate objectives must be considered. The pilot desires rapid, precise, and decoupled response to his control inputs, so that natural objective functions for computer-aided design (CAD) are computable functions that are useful measures of the speed, stability, and coupling of the responses. These response properties are often referred to as the handling qualities or flying qualities of the airplane. The military has developed a set of specifications for a number of handling quality functions, and the CAD research described in this paper uses objective functions based on these military handling qualities criteria. Additional design objective functions have been developed to avoid control limiting, since there are always limits on available control in any real system, and limiting can be destabilizing in an automatic control system. Another important property of a good design is that it be “robust”; that is, the design objectives should be insensitive to significant uncertainties in system parameters. In fact, such insensitivity is an essential property of any well-designed feedback system. Therefore, a vector of “stochastic sensitivity” functions is defined as the vector of probabilities that each “deterministic” objective violate specified requirement limits, and decreasing sensitivity is considered a design objective. If both the deterministic objectives (the nominal or expected values) and their sensitivities are considered in the design process, the number of objective functions is doubled. Moreover, modern airplanes operate over a wide range of speed and altitude, and the linearized differential equations that are used to describe the response to controls (the plant dynamic models) are different at each flight condition.

Nonlinear decoupled control synthesis for maneuvering aircraft

A control law for decoupling roll rate, angle of attack and sideslip in rapid, nonlinear airplane maneuvers is derived. For simplicity, only moments caused by ailerons, rudder and elevator are considered, and control forces are neglected. Simulated responses of the closed loop system, including the control forces, show that the neglected forces have no significant effects and that large, simultaneous lateral and longitudinal maneuvers can be precisely performed. The violent divergences which occur in open-loop maneuvers of this type are eliminated by the decoupling. The control law showed little sensitivity to 20 percent perturbation in three important stability derivatives.

Nonlinear programing in design of control systems with specified handling qualities

A method is described for using nonlinear programing in the computer-aided design of airplane control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector (instead of attempting to combine them into a single scalar criterion, as is usually done), and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter airplane, in which the requirements vector is chosen from the official handling-qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains. The choice of the final design for each case is not unique but depends on the designers decision as to which achievable set of requirements levels represents the best for that system. Results indicate that constant gain systems can substantially exceed the highest required levels of handling qualities in all design flight conditions of the example considered. The role of the designer as a decision maker, interacting with the computer program, is discussed. Advantages of this type of designer-computer interaction are emphasized. Desirable extensions of the method are indicated.