Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

2019 ◽  
Vol 2 (2) ◽  
pp. 2
Author(s):  
Denis Mosconi ◽  
Adriano Almeida Gonçalves Siqueira ◽  
Everthon Silva Fonseca
Keyword(s):  
Feedback Loop ◽  
Inverse Dynamics ◽  
Robot Manipulator ◽  
Linear Quadratic Regulator ◽  
Robotic Systems ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
End Effector ◽  
The Right

To ensure the correct positioning of the end-effector of robot manipulators is one of the most important objectives of the robotic systems control. Lack of reliability in tracking the reference trajectory, as well as in the desired final positioning compromises the quality of the task to be performed, even causing accidents. The purpose of this work was to propose an optimal controller with an inner loop based on the dynamic model of the manipulator and a feedback loop based on the Linear Quadratic Regulator, in order to ensure that the end effector is in the right place, at the right time. The controller was compared to the conventional PID, presenting better performance, both in the transient response, eliminating overshoot, and steady-state, eliminating the stationary error.

scholarly journals Tuning of a Linear-Quadratic Stabilization System for an Anti-Aircraft Missile

Aerospace ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 48
Author(s):  
Witold Bużantowicz
Keyword(s):  
Analytical Solutions ◽  
Feedback Loop ◽  
Linear Quadratic Regulator ◽  
Added Value ◽  
Tuning Parameter ◽  
Stabilization System ◽  
Linear Quadratic ◽  
Quadratic Stabilization ◽  
Novel Method ◽  
Selection Of

A description is given of an application of a linear-quadratic regulator (LQR) for stabilizing the characteristics of an anti-aircraft missile, and an analytical method of selecting the weighting elements of the gain matrix in feedback loop is proposed. A novel method of LQR tuning via a single parameter ς was proposed and tested. The article supplements and develops the topics addressed in the author’s previous work. Its added value includes the observation that the solutions obtained are symmetric pairs, and that the tuning parameter ς proposed for the designed linear-quadratic regulator enables the selection of suitable parameters for the airframe stabilizing loop for the majority of the analytical solutions of the considered Riccati equation.

scholarly journals DYNAMICS BASED CONTROL OF A SKID STEERING MOBILE ROBOT

2016 ◽  
Vol 9 (2) ◽  
pp. 70 ◽  
Author(s):  
Osama Elshazly ◽  
Hossam Abbas ◽  
Zakarya Zyada
Keyword(s):  
Mobile Robot ◽  
Inverse Dynamics ◽  
Linear Quadratic Regulator ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Lqr Control ◽  
Control Schemes ◽  
Skid Steering ◽  
Drive Model

In this paper, development of a reduced order, augmented dynamics-drive model that combines both the dynamics and drive subsystems of the skid steering mobile robot (SSMR) is presented. A Linear Quadratic Regulator (LQR) control algorithm with feed-forward compensation of the disturbances part included in the reduced order augmented dynamics-drive model is designed. The proposed controller has many advantages such as its simplicity in terms of design and implementation in comparison with complex nonlinear control schemes that are usually designed for this system. Moreover, the good performance is also provided by the controller for the SSMR comparable with a nonlinear controller based on the inverse dynamics which depends on the availability of an accurate model describing the system. Simulation results illustrate the effectiveness and enhancement provided by the proposed controller.

Optimal Error-Clamping Design for Position-Based Visual Servoing of a 2-DOF Model Helicopter

2011 ◽  
Author(s):  
M. Alizadeh ◽  
C. Ratanasawanya ◽  
M. Mehrandezh ◽  
R. Paranjape
Keyword(s):  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Physical Space ◽  
Linear Quadratic Regulator ◽  
Image Plane ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Feed Forward ◽  
Model Helicopter

A vision-based servoing technique is proposed for a 2 degrees-of-freedom (dof) model helicopter equipped with a monocular vision system. In general, these techniques can be categorized as image- and position-based, where the task error is defined in the image plane in the former and in the physical space in the latter. The 2-dof model helicopter requires a configuration-dependent feed-forward control to compensate for gravitational forces when servoing on a ground target. Therefore, a position-based visual servoing deems more appropriate for precision control. Image information collected from a ground object, with known geometry a priori, is used to calculate the desired pose of the camera and correspondingly the desired joint angles of the model helicopter. To assure a smooth servoing, the task error is parameterized, using the information obtained from the linearaized image Jacobian, and time scaled to form a moving reference trajectory. At the higher level, a Linear Quadratic Regulator (LQR), augmented with a feed-forward term and an integrator, is used to track this trajectory. The discretization of the reference trajectory is achieved by an error-clamping strategy for optimal performance. The proposed technique was tested on a 2-dof model helicopter capable of pitch and yaw maneuvers carrying a light-weight off-the-shelf video camera. The test results show that the optimized controller can servo the model helicopter to a hovering pose for an image acquisition rate of as low as 2 frames per second.

An automatic system for a helicopter autopilot performance evaluation

2019 ◽  
Vol 91 (6) ◽  
pp. 880-885 ◽  
Author(s):  
Antoni Kopyt ◽  
Sebastian Topczewski ◽  
Marcin Zugaj ◽  
Przemyslaw Bibik
Keyword(s):  
Performance Evaluation ◽  
Flight Control ◽  
Automatic System ◽  
Control Algorithm ◽  
Linear Quadratic Regulator ◽  
Algorithm Analysis ◽  
Evaluation Methodology ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Content Type

Purpose The purpose of this paper is to elaborate and develop an automatic system for automatic flight control system (AFCS) performance evaluation. Consequently, the developed AFCS algorithm is implemented and tested in a virtual environment on one of the mission task elements (MTEs) described in Aeronautical Design Standard 33 (ADS-33) performance specification. Design/methodology/approach Control algorithm is based on the Linear Quadratic Regulator (LQR) which is adopted to work as a controller in this case. Developed controller allows for automatic flight of the helicopter via desired three-dimensional trajectory by calculating iteratively deviations between desired and actual helicopter position and multiplying it by gains obtained from the LQR methodology. For the AFCS algorithm validation, the objective data analysis is done based on specified task accomplishment requirements, reference trajectory and actual flight parameters. Findings In the paper, a description of an automatic flight control algorithm for small helicopter and its evaluation methodology is presented. Necessary information about helicopter dynamic model is included. The test and algorithm analysis are performed on a slalom maneuver, on which the handling qualities are calculated. Practical implications Developed automatic flight control algorithm can be adapted and used in autopilot for a small helicopter. Methodology of evaluation of an AFCS performance can be used in different applications and cases. Originality/value In the paper, an automatic flight control algorithm for small helicopter and solution for the validation of developed AFCS algorithms are presented.

Fuzzy Logic Control for an Integrated System of a Micro-Manipulator with a Single Flexible Beam

2004 ◽  
Vol 10 (5) ◽  
pp. 755-776 ◽  
Author(s):  
N. G. Chalhoub ◽  
B. A. Bazzi
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic Controller ◽  
Angular Displacement ◽  
Digital Simulation ◽  
Linear Quadratic Regulator ◽  
Integrated System ◽  
Flexible Beam ◽  
Linear Quadratic ◽  
End Effector ◽  
Micro Manipulator

The use of lightweight robotic manipulators in advanced assembly and manufacturing applications is hindered by the end-effector positional inaccuracies induced by the structural deformations of the arm. To address this problem, a macro- and micro-manipulator system is considered herein. Three rigid and flexible motion controllers, consisting of an integral plus state feedback controller (ISFC), linear quadratic regulator with an integral action (LQI) and a fuzzy logic controller (FLC), have been implemented in this study. The performances of these controllers are compared based on achieving zero steady-state error in the rigid body angular displacement of the beam, damping out the unwanted vibrations, rendering the end-effector insensitive to the vibrations of the arm, and avoiding excessive control torque requirements. The digital simulation results demonstrate the superiority of the FLC over the ISFC and LQI in damping out the vibrations of the beam and reducing the gripper positional inaccuracies while requiring relatively smaller control torques. Furthermore, the results clearly demonstrate the robustness of the FLC to significant variations in the payload mass.

Dynamics and Trajectory Tracking Control of a Two-Link Robot Manipulator

2004 ◽  
Vol 10 (10) ◽  
pp. 1415-1440 ◽  
Author(s):  
Anthony Green ◽  
Jurek Z. Sasiadek
Keyword(s):  
Fuzzy Logic ◽  
Time Delay ◽  
Inverse Dynamics ◽  
Position Control ◽  
Robot Manipulator ◽  
Phase Response ◽  
Control Law ◽  
Minimum Phase ◽  
Linear Quadratic ◽  
Trajectory Tracking Control

Operational problems with robot manipulators in space relate to several factors, most importantly, structural flexibility and subsequent difficulties with their position control. In this paper we present control methods for endpoint tracking of a 12.6 × 12.6m2 trajectory by a two-link robot manipulator. Initially, a manipulator with rigid links is modeled using inverse dynamics, a linear quadratic regulator and fuzzy logic schemes actuated by a Jacobian transpose control law computed using dominant cantilever and pinned-pinned assumed mode frequencies. The inverse dynamics model is pursued further to study a manipulator with flexible links where nonlinear rigid-link dynamics are coupled with dominant assumed modes for cantilever and pinned-pinned beams. A time delay in the feedback control loop represents elastic wave travel time along the links to generate non-minimum phase response. A time delay acting on control commands ameliorates non-minimum phase response. Finally, a fuzzy logic system outputs a variable to adapt the control law in response to elastic deformation inputs. Results show greater endpoint position control accuracy using a flexible inverse dynamics robot model combined with a fuzzy logic adapted control law and time delays than could be obtained for the rigid dynamics models.

Variable-Velocity Exponential Input Shaping for Position Controlled Robotic Systems

2010 ◽  
Author(s):  
P. Iravani ◽  
M. N. Sahinkaya
Keyword(s):  
Inverse Dynamics ◽  
Vibration Reduction ◽  
Robotic Systems ◽  
Input Shaping ◽  
Control Input ◽  
End Effector ◽  
Flexible System ◽  
Flexible Loads ◽  
New Form ◽  
Point To Point

This paper demonstrates a new form of Input Shaping for vibration reduction applied to robotic systems that manipulate flexible loads. The method is based on using an exponential function to define asymptotic and vibration-free trajectories for the flexible system. The required control input is calculated analytically by using inverse dynamics which ensures the desired end-effector trajectory. The method is demonstrated experimentally on the control of point-to-point movements of a robotic manipulator.

Motion planning of spacecraft with obstacle avoidance under low uncertainty using the improved equal-collision-probability-curve and improved linear quadratic regulator strategy

2019 ◽  
Vol 233 (14) ◽  
pp. 5456-5467
Author(s):  
Wang Yi ◽  
Chen Xiaoqian ◽  
Bai Yuzhu ◽  
Cao Lu ◽  
Zhu Xiaozhou
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Linear Quadratic Regulator ◽  
Collision Probability ◽  
Planning Problem ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Probability Curve ◽  
Proximity Operations ◽  
Low Uncertainty

In terms of the motion planning problem of spacecraft proximity operations with obstacle avoidance under low uncertainty, the improved equal-collision-probability-curve and improved linear quadratic regulator (IECPC-ILQR) strategy is proposed. Firstly, the novel function of the IECPC algorithm is developed to generate the avoidance control impulse. Subsequently, the ILQR is designed to track the reference trajectory. Furthermore, combining the improved ECPC algorithm with the ILQR controller, the composite controller of the IECPC-ILQR strategy is obtained and is implemented on the chaser spacecraft. Compared with the traditional ECPC algorithm, the IECPC-ILQR strategy can avoid collision in the presence of low uncertainty. Furthermore, the proposed avoidance strategy can obtain higher control precision while requiring the same fuel. Finally, numerical simulations verify the effectiveness of the proposed IECPC-ILQR strategy.

Trajectory evaluation for manipulators with motion and sensor uncertainties

2017 ◽  
Vol 44 (5) ◽  
pp. 658-670 ◽  
Author(s):  
Ruolong Qi ◽  
Weijia Zhou ◽  
Wang Tiejun
Keyword(s):  
Design Methodology ◽  
Prior Probability ◽  
Probability Distributions ◽  
Space Station ◽  
Linear Quadratic Regulator ◽  
Goal Area ◽  
Linear Quadratic ◽  
End Effector ◽  
Content Type ◽  
Entire Trajectory

Purpose Uncertainty can arise for a manipulator because its motion can deviate unpredictably from the assumed dynamical model and because sensors might provide information regarding the system state that is imperfect because of noise and imprecise measurement. This paper aims to propose a method to estimate the probable error ranges of the entire trajectory for a manipulator with motion and sensor uncertainties. The aims are to evaluate whether a manipulator can safely avoid all obstacles under uncertain conditions and to determine the probability that the end effector arrives at its goal area. Design/methodology/approach An effective, analytical method is presented to evaluate the trajectory error correctly, and a motion plan was executed using Gaussian models by considering sensor and motion uncertainties. The method used an integrated algorithm that combined a Gaussian error model with an extended Kalman filter and a linear–quadratic regulator. Iterative linearization of the nonlinear dynamics was used around every section of the trajectory to derive all of the prior probability distributions before execution. Findings Simulation and experimental results indicate that the proposed trajectory planning method based on the motion and sensor uncertainties is indeed highly convenient and efficient. Originality/value The proposed approach is applicable to manipulators with motion and sensor uncertainties. It helps determine the error distribution of the predefined trajectory. Based on the evaluation results, the most appropriate trajectory can be selected among many predefined trajectories according to the error ranges and the probability of arriving at the goal area. The method has been successfully applied to a manipulator operating on the Chinese Space Station.

scholarly journals Inverse optimal control from incomplete trajectory observations

2021 ◽  
pp. 027836492199638
Author(s):  
Wanxin Jin ◽  
Dana Kulić ◽  
Shaoshuai Mou ◽  
Sandra Hirche
Keyword(s):  
Optimal Control ◽  
Objective Function ◽  
Control Algorithm ◽  
Robot Manipulator ◽  
Linear Quadratic Regulator ◽  
Inverse Optimal Control ◽  
Linear Quadratic ◽  
System States ◽  
Segment Data ◽  
The Relationship

This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) with unknown weights, and the observed data is a segment of a trajectory of system states and inputs. The proposed technique introduces the concept of the recovery matrix to establish the relationship between any available segment of the trajectory and the weights of given candidate features. The rank of the recovery matrix indicates whether a subset of relevant features can be found among the candidate features and the corresponding weights can be learned from the segment data. The recovery matrix can be obtained iteratively and its rank non-decreasing property shows that additional observations may contribute to the objective learning. Based on the recovery matrix, a method for using incomplete trajectory observations to learn the weights of selected features is established, and an incremental inverse optimal control algorithm is developed by automatically finding the minimal required observation. The effectiveness of the proposed method is demonstrated on a linear quadratic regulator system and a simulated robot manipulator.

Sign in / Sign up

Export Citation Format

Share Document