On Optimal Control Laws for a Class of Constrained Dynamical Systems (With Application to Control of Bipedal Locomotion)

1977 ◽  
Vol 99 (2) ◽  
pp. 98-102 ◽  
Author(s):  
M. A. Townsend ◽  
T. C. Tsai
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Inequality Constraints ◽  
Control Law ◽  
Bipedal Locomotion ◽  
Control Laws ◽  
Smooth Control ◽  
Proper Formulation ◽  
Constrained Dynamical Systems ◽  
Dynamical Constraints

The physical and dynamical constraints of a constrained dynamical system are related to system controllability and stability. Proper formulation of these inequality constraints and treatment of the active ones leads to stabilizing controls with relatively smooth control efforts—in all cases, control laws. These approaches were useful in a study of the biomechanics of climbing and descending gaits by mathematical synthesis techniques, necessitated by the increased importance of terrain and lower extremity kinematics and incomplete specification of the tasks. The general criteria entail no uniqueness requirements on system motions and controls, although for the most common (and probably most desirable) condition of the constraints (fewer active constraints than system degrees of freedom) an “optimal” control law can be derived. Two examples are presented, and some general discussion is given relating mainly to the control of biped locomotion.

Scheduling Strategy of Multiple Semi-Active Controllers With Information on the Disturbance and the Structural Response

2016 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Katsuaki Sunakoda
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Active Control ◽  
Structural Response ◽  
Design Parameters ◽  
Control Law ◽  
Control Performance ◽  
Multiple Control ◽  
Control Laws ◽  
Scheduling Strategy

A scheduling strategy of multiple semi-active control laws for various earthquake disturbances is proposed to maximize the control performance. Generally, the semi-active controller for a given structural system is designed as a single control law and the single control law is used for all the forthcoming earthquake disturbances. It means that the general semi-active control should be designed to achieve a certain degree of the control performance for all the assumed disturbances with various time and/or frequency characteristics. Such requirement on the performance robustness becomes a constraint to obtain the optimal control performance. We propose a scheduling strategy of multiple semi-active control laws. Each semi-active control law is designed to achieve the optimal performance for a single earthquake disturbance. Such optimal control laws are scheduled with the available data in the control system. As the scheduling mechanism of the multiple control laws, a command signal generator (CSG) is defined in the control system. An artificial neural network (ANN) is adopted as the CSG. The ANN-based CSG works as an interpolator of the multiple control laws. Design parameters in the CSG are optimized with the genetic algorithm (GA). Simulation study shows the effectiveness of the approach.

Minimum Energy Control of Redundant Systems Using Evolutionary Bi-Level Optimization

2018 ◽  
Author(s):  
Uriel Nusbaum ◽  
Miri Weiss Cohen ◽  
Yoram Halevi
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Energy Savings ◽  
Level Structure ◽  
Minimum Energy ◽  
Inequality Constraints ◽  
Constrained Optimal Control ◽  
Reduced Order ◽  
Control Comparison ◽  
Level Problem

Redundant manipulators are mechanical systems with more degrees of freedom than required for their task. The paper considers the problem of energy minimization, given a required task, for such systems. The problem is formulated as a constrained optimal control with additional inequality constraints. A dynamic projection enables transforming the problem into an equivalent unconstrained, reduced order one. The solution scheme presented here combines the problems of path planning and tracking control. It includes decomposition of the problem into a bi-level structure. The parametric, higher-level problem is solved using a genetic algorithm and the lower level one is solved using optimal control. Comparison with full optimal control solutions shows the superiority of the combined evolutionary algorithm in terms of computational feasibility and overall energy savings.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Robust Trajectory Following Control of Robotic Systems

1985 ◽  
Vol 107 (4) ◽  
pp. 308-315 ◽  
Author(s):  
S. N. Singh ◽  
A. A. Schy
Keyword(s):  
Degrees Of Freedom ◽  
Digital Simulation ◽  
Robotic Systems ◽  
Control Law ◽  
Robot Arm ◽  
Control Laws ◽  
Payload Uncertainty ◽  
Trajectory Following ◽  
And Control ◽  
Three Degrees Of Freedom

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.

Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method

1999 ◽  
Vol 121 (2) ◽  
pp. 174-182 ◽  
Author(s):  
N. Tanaka ◽  
Y. Kikushima
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Point ◽  
Control Law ◽  
Bernoulli Beam ◽  
Control Laws ◽  
Reflected Waves ◽  
Feedback Control Systems ◽  
Active Wave ◽  
Euler Bernoulli Beam

This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal control law that is likely to be non-causal, a “classical” velocity feedback control law (Balas, 1979) widely used in a vibration control engineering is applied, revealing a substantial shortcoming. Introduction of a “classical” displacement feedback to the velocity is found to realize the optimal control law in a restricted frequency range. Finally, two kinds of stability verification for closed feedback control systems are presented for distributed parameter structures.

scholarly journals A Novel Adaptive Gain of Optimal Sliding Mode Controller for Linear Time-Varying Systems

2019 ◽  
Vol 9 (23) ◽  
pp. 5050 ◽  
Author(s):  
Do Xuan Phu ◽  
Van Mien ◽  
Seung-Bok Choi
Keyword(s):  
Optimal Control ◽  
Sliding Mode ◽  
Linear Time ◽  
Control Law ◽  
Time Varying ◽  
Control Laws ◽  
Control Gain ◽  
Salient Characteristic ◽  
Time Varying Systems ◽  
Main Input

In this study, a new optimal control law associated with the sliding mode control is developed for the linear time-varying system based on the Bolza-Meyer criterion. The salient characteristic of the controller proposed in this work is to have adjustable gains in which the gain values can be larger than 1. This leads to the enhancement of control performances with the given cost function. It is noted here that conventional optimal control laws have a constant gain of 1 or less than 1, and hence, control performances such as the convergence speed are not satisfactory. After formulating the proposed optimal control law for linear time-varying systems, several illustrative examples are adopted and control performances were evaluated to show some benefits of the proposed controller. In particular, three crucial index values of control gain index, main input control index and the state index were investigated. Among illustrative examples, one is related to vibration control problem of the vehicle seat suspension system with magnetorheological (MR) damper. This example is specially treated to evaluate the practical applicability of the proposed optimal controller by considering the measured road profiles; two different random road excitations.

scholarly journals Adaptive Fuzzy Sliding Mode Tracking Control of Uncertain Underactuated Nonlinear Systems: A Comparative Study

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Faten Baklouti ◽  
Sinda Aloui ◽  
Abdessattar Chaari
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Underactuated System ◽  
Control Law ◽  
Sliding Mode Controller ◽  
Fuzzy Logic Systems ◽  
Control Laws ◽  
Adaptive Fuzzy ◽  
Hierarchical Sliding Mode

The trajectory tracking of underactuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical sliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding surfaces and chattering by adopting different reaching laws. The unknown system functions are approximated by fuzzy logic systems and free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in this paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the chattering phenomenon. The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller and two other control laws which keep the coupling in the underactuated system. The tracking performances of each control law are evaluated. Simulation examples including different amplitudes of external disturbances are made.

Backward Path Tracking of Mobile Robot with Two Trailers

2014 ◽  
Vol 716-717 ◽  
pp. 1512-1517
Author(s):  
Yu Ma ◽  
Yong Zhang ◽  
Jin Cheng ◽  
Qin Jun Zhao
Keyword(s):  
Mobile Robot ◽  
Tracking Control ◽  
Path Tracking ◽  
Control Law ◽  
Control Laws ◽  
New Approach ◽  
Smooth Control ◽  
The Social ◽  
Continuous Progress ◽  
Nonlinear Smooth

With the social development and the continuous progress of science and technology, the mobile robots can greatly improve efficiency, reduce costs, many of these applications can be attributed to the backward path tracking control problem. A controller for backward path tracking of mobile robot with two trailers is addressed in this paper. The paper presents a new approach to stabilizing the system in backward motion by controlling the orientation angles of the two trailers. Nonlinear smooth control laws for orientations of the trailers with asymptotic stability in backward motion are then proposed. The result simulated in Simulink illustrates the effectiveness of the control law and the controller.

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