Etsujiro Shimemura

Shape control of manipulators with hyper degrees of freedom

This paper provides a theoretical framework for controlling a manipulator with hyper degrees of freedom (HDOF). An HDOF manipulator has the capability to achieve various kinds of tasks. To make full use of its capability, shape control is proposed here; that is, not only the tip of a manipulator, but also its whole body is controlled. To formulate control objectives for shape control, we define a shape correspondence between an HDOF manipulator and a spatial curve that prescribes a desired shape. The shape correspondence is defined by using solutions of a nonlinear optimization problem termed the shape-inverse problem. We give theorems on the existence of the solutions, and on an existence region that allows us to convert shape-control problems into more tractable ones. A shape-regulation control problem is considered first to bring an HDOF manipulator onto a given time-invariant curve. The idea of estimating the desired curve parameters is the crucial key to solving the problem by Lyapunov design. The derived shape-regulation law includes the estimator, which infers the desired curve parameters corresponding to the desired joint positions on the curve. The idea of the desired curve-parameter estimation is also effective for shape tracking where a time-varying curve is used for prescribing a moving desired shape. Considering an estimator with second-order dynamics enables us to find two shape-tracking control laws by utilizing conventional tracking methods in manipulator control. We show the simulation results of applying the derived shape-tracking control laws to a 20-DOF manipulator.

On Application of the Descriptor Form to Design of Gain Scheduling System

The descriptor form provides system representations that preserve structure of systems along with static constraints on descriptor variables. Based on the descriptor-form representations of LPV (linear parameter varying) -systems, this paper proposes an approach to gain-scheduling controller synthesis. First, we show a descriptor form with scheduling parameters on the coefficient matrices and discuss using it as a model of LPV-systems. Next, we give a synthesis method of quadratically stabilizing LPV-controllers via solving LMIs for both state-feedback and output-feedback systems.

Computation of optimal feedback gains for time-varying LQ optimal control

A computational method is proposed to compute the optimal feedback control law of time-varying linear quadratic optimal control problem. The idea of the method is to use Chebyshev polynomials of the first type and their differentiation operational matrix to solve the matrix Riccati equation. To show the effectiveness of the proposed method, the simulation result of an example is shown.

Exponential stabilization of systems with time-delay by optimal memoryless feedback

A method to construct a memoryless feedback law for system with time-delay in states is proposed. A feedback gain is calculated with a solution of a matrix Riccati equation. It is shown that the memoryless feedback law asymptotically stabilizes the closed loop system and it is an optimal control for some quadratic cost functional. Then, an auxiliary system is introduced and a feedback gain is calculated in the same way. Using this gain, a feedback law for the original plant is re-constructed. It is shown that it gives the resulting closed loop system a pre-assigned exponential stability, and moreover, it is an optimal control for another cost functional. A sufficient condition for the construction of the feedback is presented. A design example is shown, and a numerical simulation is performed.

Control of serial rigid link manipulators with hyper degrees of freedom: shape control by a homogeneously decentralized scheme and its experiment

In this paper, a new shape control law is proposed to bring a serial rigid link manipulator with hyper degrees of freedom into a specified shape. Shape control is one of the most characteristic controls for a hyper degrees of freedom manipulator. This control law is derived by the Lyapunov design method. A homogeneously decentralized control scheme is also proposed for practical application of the control law to a hyper degrees of freedom manipulator, and it is shown that the derived control law can be realized in a homogeneously decentralized control scheme. The effectiveness of this control law is verified by a hardware model experiment.

Optimal closed loop control for nonlinear systems using Chebyshev polynomials

A method is proposed to construct the optimal feedback control law of a nonlinear optimal control problem. The method is based on two steps: the first step is to determine the open loop optimal control and trajectories, by using the quasilinearization and the state variables parameterization via Chebyshev polynomials of the first type; the second step is to use the results of the last quasilinearization iteration, when acceptable convergence error is achieved, to obtain the optimal feedback control law. To show the effectiveness of the proposed method, the simulation results of a nonlinear optimal control problem are shown.

Construction of optimal feedback control for nonlinear systems via Chebyshev polynomials

A method is proposed to determine the optimal feedback control law of a class of nonlinear optimal control problems. The method is based on two steps. The first step is to determine the open-hop optimal control and trajectories, by using the quasilinearization and the state variables parametrization via Chebyshev polynomials of the first type. Therefore the nonlinear optimal control problem is replaced by a sequence of small quadratic programming problems which can easily be solved. The second step is to use the results of the last quasilinearization iteration, when an acceptable convergence error is achieved, to obtain the optimal feedback control law. To this end, the matrix Riccati equation and another n linear differential equations are solved using the Chebyshev polynomials of the first type. Moreover, the differentiation operational matrix of Chebyshev polynomials is introduced. To show the effectiveness of the proposed method, the simulation results of a nonlinear optimal control problem are shown.

H2-optimal controller reduction by frequency-weighted balanced realization

In this paper, we propose a new controller reduction method which considers maintaining the index value of H2-optimal controller. In the method, a frequency-weighted balanced realization technique developed by Enns is employed to obtain low order controllers. The fractional representation is used to reduce the order of unstable controllers effectively. To illustrate the effectiveness of our method, two numerical examples are presented.

LQ regulator of systems with time-delay by memoryless feedback

A memoryless feedback law is constructed for a linear system with time-delay in states. It is shown that the resulting closed loop system is asymptotically stable, and it is a linear quadratic regulator for some cost functional.

Gain margin of an LQ regulator by the lumped-parameter-part control

The vibration control of a cantilever beam with an active mass damper is considered. A hybrid parameter system model is introduced. A linear quadratic regulator is constructed by the lumped-parameter-part feedback, and a stability condition against a nonlinear perturbation in the input channel is derived.