scholarly journals Reachability Analysis for Robustness Evaluation of the Sit-to-Stand Movement for Powered Lower Limb Orthoses

2018 ◽  
Author(s):  
Octavio Narvaez-Aroche ◽  
Andrew Packard ◽  
Pierre-Jean Meyer ◽  
Murat Arcak
Keyword(s):  
Lower Limb ◽  
Center Of Mass ◽  
Linear Quadratic Regulator ◽  
The State ◽  
Reachable Sets ◽  
Linear Quadratic ◽  
Initial State ◽  
Worst Case ◽  
Sit To Stand ◽  
Finite Time Horizon

A sensitivity-based approach for computing over-approximations of reachable sets, in the presence of constant parameter uncertainty and a single initial state, is used to analyze a three-link planar robot modeling a Powered Lower Limb Orthosis and its user. Given the nature of the mappings relating the state and parameters of the system with the input, and output describing the trajectories of its Center of Mass, reachable sets for their respective spaces can be obtained relying on the sensitivities of the nonlinear closed-loop dynamics in the state space. These over-approximations are used to evaluate the worst-case performances of a finite time horizon linear-quadratic regulator for controlling the ascending phase of the Sit-To-Stand movement.

scholarly journals Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Alain G. de Souza ◽  
Luiz C. G. de Souza
Keyword(s):  
Control System ◽  
Attitude Control ◽  
Center Of Mass ◽  
Rigid Motion ◽  
Linear Quadratic Regulator ◽  
Comparative Investigation ◽  
Attitude Control System ◽  
Linear Quadratic ◽  
Deformable Structure ◽  
Fuel Slosh

The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.

scholarly journals Terrain-Perception-Free Quadrupedal Spinning Locomotion on Versatile Terrains: Modeling, Analysis, and Experimental Validation

2021 ◽  
Vol 8 ◽  
Author(s):  
Hongwu Zhu ◽  
Dong Wang ◽  
Nathan Boyd ◽  
Ziyi Zhou ◽  
Lecheng Ruan ◽  
...  
Keyword(s):  
Motion Tracking ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Linear Quadratic Regulator ◽  
Small Scale ◽  
Small Range ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Uneven Terrain ◽  
Quadruped Robots

Dynamic quadrupedal locomotion over rough terrains reveals remarkable progress over the last few decades. Small-scale quadruped robots are adequately flexible and adaptable to traverse uneven terrains along the sagittal direction, such as slopes and stairs. To accomplish autonomous locomotion navigation in complex environments, spinning is a fundamental yet indispensable functionality for legged robots. However, spinning behaviors of quadruped robots on uneven terrain often exhibit position drifts. Motivated by this problem, this study presents an algorithmic method to enable accurate spinning motions over uneven terrain and constrain the spinning radius of the center of mass (CoM) to be bounded within a small range to minimize the drift risks. A modified spherical foot kinematics representation is proposed to improve the foot kinematic model and rolling dynamics of the quadruped during locomotion. A CoM planner is proposed to generate a stable spinning motion based on projected stability margins. Accurate motion tracking is accomplished with linear quadratic regulator (LQR) to bind the position drift during the spinning movement. Experiments are conducted on a small-scale quadruped robot and the effectiveness of the proposed method is verified on versatile terrains including flat ground, stairs, and slopes.

Optimal Roll Control of a Single-Unit Lorry

1996 ◽  
Vol 210 (1) ◽  
pp. 45-55 ◽  
Author(s):  
R C Lin ◽  
D Cebon ◽  
D J Cole
Keyword(s):  
Single Unit ◽  
Load Transfer ◽  
Linear Quadratic Regulator ◽  
Lateral Acceleration ◽  
Hydraulic Actuator ◽  
Linear Quadratic ◽  
Mean Power ◽  
Worst Case ◽  
Limited Bandwidth ◽  
Roll Control

Lateral acceleration control and linear quadratic regulator (LQR) theory are used to design active roll control systems for heavy goods vehicles. The suspension consists of a limited bandwidth hydraulic actuator in series with an anti-roll bar. The procedure used to determine suitable controller gains is described. The simulation results show that roll control of a single-unit lorry requires an actuator bandwidth of 6 Hz and mean power of approximately 17 kW for a ‘worst case’ random steering input. The static roll-over threshold of this vehicle is increased by 66 per cent when compared with the same vehicle with passive suspensions and the r.m.s. lateral load transfer is reduced by 34 per cent for a typical random steering input.

scholarly journals Performance Evaluation of Pole Placement and Linear Quadratic Regulator Strategies Designed for Mass-Spring-Damper System Based on Simulated Annealing and Ant Colony Optimization

2021 ◽  
Vol 27 (11) ◽  
pp. 15-31
Author(s):  
Huthaifa Al-Khazraji ◽  
Luay T. Rasheed
Keyword(s):  
Performance Evaluation ◽  
Simulated Annealing ◽  
State Feedback ◽  
Linear Quadratic Regulator ◽  
The State ◽  
Ant Colony ◽  
System Stability ◽  
Pole Placement ◽  
Linear Quadratic ◽  
Mass Spring

This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab software has been used for simulations and performance analysis. The results show the superiority of the state feedback based on the LQR controller in improving the system stability, reducing settling time, and reducing maximum overshoot. Furthermore, AC optimization shows significant advantages for optimizing the parameters of PP and LQR and reducing the fitness value in comparison with SA optimization

A Study of Effective Prediction Methods of the State-Action Pair for Robot Control Using Online SVR

2015 ◽  
Vol 27 (5) ◽  
pp. 469-479 ◽  
Author(s):  
Masashi Sugimoto ◽  
◽  
Kentarou Kurashige
Keyword(s):  
Linear Quadratic Regulator ◽  
The State ◽  
Support Vector ◽  
Linear Quadratic ◽  
Appropriate Behavior ◽  
State Action ◽  
Inverted Pendulum Model ◽  
Future State ◽  
Course Of Action ◽  
The Future

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270005/02.jpg"" width=""300"" /> Prediction of future state and action</div> In order to work effectively, a robot should be able to adapt to different environments by deciding its correct course of action according to the situation, using determinants other than pre-registered commands. For this purpose, the ability to predict the future state of a robot would be effective. On the other hand, the future state of a robot varies infinitely if it depends on its current action. Therefore, it is difficult to predict only the future state. Thus, it is important to simultaneously predict the state and the action that the robot will adopt. The purpose of this study was to investigate the prediction of the advanced future state and action of a robot. In this paper, the results of the study are reported and methods that allow a robot to decide its appropriate behavior quickly, according to the predicted future state are discussed. As an application example for evaluating the proposed method, the inverted pendulum model is used and the prediction results are compared with the robot’s actual responses. Then, two methods will be discussed for predicting the robot’s state and action. To perform state and action prediction, two methods are used, firstly the Online SVR (Support Vector Regression) and secondly Online SVR and the LQR (Linear Quadratic Regulator). </span>

scholarly journals On Decentralized Optimization for a Class of Multisubsystem Codesign Problems

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Tianchen Liu ◽  
Shapour Azarm ◽  
Nikhil Chopra
Keyword(s):  
Optimization Model ◽  
Linear Quadratic Regulator ◽  
Plant Design ◽  
Linear Quadratic ◽  
Decentralized Optimization ◽  
Linear Equality Constraints ◽  
Physical Plant ◽  
Convex Inequality ◽  
Finite Time Horizon ◽  
And Control

Codesign refers to the process of integrating the optimization of the physical plant design and control of a system. In this paper, a new class of codesign problems with a multisubsystem architecture in both design and control is formulated and solved. Our work here extends earlier research on models and solution approaches from single system to multisubsystem codesign. In this class, the optimization model for the physical design part in each subsystem is assumed to have a convex objective function with convex inequality and linear equality constraints. The optimization model for the control part of each subsystem belongs to a class of finite time-horizon linear quadratic regulator (LQR) feedback control. A new multilevel decentralized method is proposed that can obtain optimal or near-optimal solutions for this class of codesign problems. Details of the model and approach are presented and demonstrated by a numerical as well as a more complex spring–mass–damper system example. The proposed decentralized approach has been compared with a centralized approach. Using a scalable test problem, it is shown that as the size of the problem is increased, the computation effort for the decentralized approach increases linearly while that of the centralized approach increases nonlinearly.

Minimax Output Feedback Regulators

1976 ◽  
Vol 98 (3) ◽  
pp. 270-276 ◽  
Author(s):  
T. Yahagi
Keyword(s):  
Output Feedback ◽  
Necessary Conditions ◽  
Output Feedback Control ◽  
Linear Quadratic Regulator ◽  
Recursive Formula ◽  
Performance Measure ◽  
Minimax Solution ◽  
Linear Quadratic ◽  
Initial State ◽  
Optimal Constant

The linear quadratic regulator problem is considered, and a method for obtaining an optimal output feedback control subject to a minimax performance index is presented. The optimal constant feedback matrix, which denotes the optimal constant feedback gains, is determined by minimizing the effects of the worst value of the initial state on the system performance measure. First, the necessary conditions for a minimax solution are given analytically. However, it is very difficult to determine the minimax solution directly from these necessary conditions. Then, a method for obtaining an optimal numerical solution by using a recursive formula is presented. Two iterative algorithms for the minimax solution are given. These algorithms are based on Theorem 4 and the saddle point assumption is not used. As shown in the illustrative examples the iterative solutions converge to the minimax value rapidly, and this method is useful for obtaining the minimax output feedback solution.

Polynomial-Chaos-Based Numerical Method for the LQR Problem With Uncertain Parameters in the Formulation

2010 ◽  
Author(s):  
Emmanuel Blanchard ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Numerical Method ◽  
Polynomial Chaos ◽  
Linear Quadratic Regulator ◽  
Mean Value ◽  
Optimal Controller ◽  
Linear Quadratic ◽  
Case Scenario ◽  
Worst Case ◽  
Lqr Problem ◽  
And Performance

This paper proposes a polynomial chaos based numerical method providing an optimal controller for the linear-quadratic regulator (LQR) problem when the parameters in the formulation are uncertain, i.e., a controller minimizing the mean value of the LQR cost function obtained for a certain distribution of the uncertainties which is assumed to be known. The LQR problem is written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and an iterative algorithm converges to the optimal answer. The algorithm is applied to a simple example for which the answer is already known. Polynomial chaos based methods have the advantage of being computationally much more efficient than Monte Carlo simulations. The Linear-Quadratic Regulator controller is not very well adapted to robust design, and the optimal controller does not guarantee a minimum performance or even stability for the worst case scenario. Stability robustness and performance robustness in the presence of uncertainties are therefore not guaranteed. However, this is a first step aimed at designing more judicious controllers if combined with other techniques in the future. The next logical step would be to extend this numerical method to H2 and then H-infinity problems.

Motion Planning of the Sit to Stand Movement for Powered Lower Limb Orthoses

2017 ◽  
Author(s):  
Octavio Narvaez-Aroche ◽  
Andrew Packard ◽  
Murat Arcak
Keyword(s):  
Lower Limb ◽  
Feedback Linearization ◽  
User Modeling ◽  
Center Of Mass ◽  
Angular Position ◽  
Control Allocation ◽  
Sit To Stand ◽  
Kinematic Behavior ◽  
Planar Robot ◽  
Reference Trajectories

We propose a generalizable strategy for planning the sit to stand movement of a powered lower limb orthosis and its user. Modeling the system as a three rigid link planar robot, we rely on its kinematic equations to obtain a set of transformations that allows us to compute reference trajectories for the angular positions of the links, starting from a desired kinematic behavior for the center of mass of the robot and the angular position of link 2 relative to link 1; as we consider them more suitable to define for achieving a safe sit to stand transition. We then proceed to design a tracking controller via feedback linearization and solve a constrained least-squares program to address the control allocation problem from including the loads applied by the arms of the user as inputs. We simulate two relevant STS movements to illustrate the system tracking the reference trajectories generated with our strategy, in the presence of parameter uncertainty.

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