Optimal periodic gain scheduling for bipedal walking with hybrid dynamics

Robotica ◽  
2014 ◽  
Vol 34 (8) ◽  
pp. 1811-1821
Author(s):  
M. Harel ◽  
G. Agranovich ◽  
M. Brand
Keyword(s):  
Dynamic Programming ◽  
Periodic System ◽  
Monodromy Matrix ◽  
Tracking Error ◽  
Gain Scheduling ◽  
Bipedal Walking ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Hybrid Dynamics ◽  
Linear Periodic System

SUMMARYWe present an optimal gain scheduling control design for bipedal walking with minimum tracking error. We obtained a linear approximation by linearizing the nonlinear hybrid dynamic model about a nominal periodic trajectory. This linearization allows us to identify the linear model as a linear periodic system. An optimal feedback was designed using Bellman's dynamic programming. The linear periodic system allows us to determine a linear quadratic regulator (LQR) for a single period and to set the Hamilton-Jacobi-Bellman (HJB) function in a linear quadratic form. In this way, the dynamic programming yielded an admissible continuous gain scheduling that was designed with regard to the hybrid dynamics of the system. We tuned the optimization parameters such that the tracking error and the average energy consumption are minimized. Due to linearization, we were able to examine the stability of the approximated periodic system achieved by the periodic gain according to Floquet's theory, by calculating the monodromy matrix of the closed-loop hybrid system. In addition to determining stability, the eigenvalues of this approximated monodromy matrix allowed us to evaluate the settling time of the system. This approach presents a direct method for optimal solution of locomotion control according to a given reference trajectory.

scholarly journals Finite-Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Shizheng Wan ◽  
Xiaofei Chang ◽  
Quancheng Li ◽  
Jie Yan
Keyword(s):  
Dynamic Programming ◽  
Approximate Dynamic Programming ◽  
Least Squares Method ◽  
Flight Path ◽  
Finite Horizon ◽  
Dynamic Programming Method ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Optimal Tracking ◽  
Flight Path Angle

Referring to the optimal tracking guidance of aircraft, the conventional time based kinematics model is transformed into a downrange based model by independent variable replacement. The deviations of in-flight altitude and flight path angle are penalized and corrected to achieve high precision tracking of reference trajectory. The tracking problem is solved as a linear quadratic regulator applying small perturbation theory, and the approximate dynamic programming method is used to cope with the solving of finite-horizon optimization. An actor-critic structure is established to approximate the optimal tracking controller and minimum cost function. The least squares method and Adam optimization algorithm are adopted to learn the parameters of critic network and actor network, respectively. A boosting trajectory with maximum final velocity is generated by Gauss pseudospectral method for the validation of guidance strategy. The results show that the trained feedback control parameters can effectively resist random wind disturbance, correct the initial altitude and flight path angle deviations, and achieve the goal of following a given trajectory.

scholarly journals Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Elvedin Kljuno ◽  
Robert L. Williams
Keyword(s):  
Inverse Dynamics ◽  
Reference Model ◽  
Tracking Error ◽  
Gain Scheduling ◽  
Bipedal Walking ◽  
Walking Robot ◽  
Concentrated Mass ◽  
Mass Model ◽  
Nonlinear Gain ◽  
Joint Torques

This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is necessary for better performance. The emphasis of this work is to show that the reference model can be a bipedal walking model with concentrated mass at the center of gravity, which removes the problems related to design of a pseudo-inverse system. Another significance of this approach is the reduced calculation requirements due to the simplified procedure of nominal joint torques calculation. Kinematic and dynamic analysis is discussed including results for joint torques and ground force necessary to implement a prescribed walking motion. This analysis is accompanied by a comparison with experimental data. An inverse plant and a tracking error linearization-based controller design approach is described. We propose a novel combination of a nonlinear gain scheduling with a concentrated mass model for the MIMO bipedal robot system.

scholarly journals Implementation and intelligent gain tuning feedback–based optimal torque control of a rotary parallel robot

2021 ◽  
pp. 107754632110191
Author(s):  
Farzam Tajdari ◽  
Naeim Ebrahimi Toulkani
Keyword(s):  
Real Time ◽  
Tracking Error ◽  
Parallel Robot ◽  
Torque Control ◽  
Test Bed ◽  
Linear Quadratic ◽  
Control Effort ◽  
The Real ◽  
Unknown Disturbances ◽  
Quadratic Integral

Aiming at operating optimally minimizing error of tracking and designing control effort, this study presents a novel generalizable methodology of an optimal torque control for a 6-degree-of-freedom Stewart platform with rotary actuators. In the proposed approach, a linear quadratic integral regulator with the least sensitivity to controller parameter choices is designed, associated with an online artificial neural network gain tuning. The nonlinear system is implemented in ADAMS, and the controller is formulated in MATLAB to minimize the real-time tracking error robustly. To validate the controller performance, MATLAB and ADAMS are linked together and the performance of the controller on the simulated system is validated as real time. Practically, the Stewart robot is fabricated and the proposed controller is implemented. The method is assessed by simulation experiments, exhibiting the viability of the developed methodology and highlighting an improvement of 45% averagely, from the optimum and zero-error convergence points of view. Consequently, the experiment results allow demonstrating the robustness of the controller method, in the presence of the motor torque saturation, the uncertainties, and unknown disturbances such as intrinsic properties of the real test bed.

scholarly journals Trajectory Tracking For Quadrotors: An Optimization-Based Planning Followed By Controlling Approach

2021 ◽  
Author(s):  
Geesara Kulathunga ◽  
Dmitry Devitt ◽  
Alexandr Klimchik
Keyword(s):  
Trajectory Tracking ◽  
Euclidean Distance ◽  
Control Policy ◽  
Multiple Shooting ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Distance Transformation ◽  
Direct Collocation ◽  
Better Than

Abstract We present an optimization-based reference trajectory tracking method for quadrotor robots for slow-speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy to Linear Quadratic Gaussian (LQG) in which Nonlinear Model Predictive Control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple-shooting (MS) is suggested over Direct-collocation (DC) for imposing constraints when modelling the NMPC. Incremental Euclidean Distance Transformation Map (EDTM) is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated, ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor’s current pose and the desired reference trajectory pose in each iteration. Finally, we evaluated the proposed method with two other approaches and showed that our proposal is better than those two in terms of reaching the goal without any collision. Additionally, we published a new dataset, which can be used for evaluating the performance of trajectory tracking algorithms.

scholarly journals A model reference adaptive variable impedance control method for robot

2021 ◽  
Vol 336 ◽  
pp. 03005
Author(s):  
Xinchao Sun ◽  
Lianyu Zhao ◽  
Zhenzhong Liu
Keyword(s):  
Real Time ◽  
Tracking Control ◽  
Control Method ◽  
Impedance Control ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Control Parameters ◽  
Model Reference ◽  
Force Tracking ◽  
Model Reference Adaptive

As a simple and effective force tracking control method, impedance control is widely used in robot contact operations. The internal control parameters of traditional impedance control are constant and cannot be corrected in real time, which will lead to instability of control system or large force tracking error. Therefore, it is difficult to be applied to the occasions requiring higher force accuracy, such as robotic medical surgery, robotic space operation and so on. To solve this problem, this paper proposes a model reference adaptive variable impedance control method, which can realize force tracking control by adjusting internal impedance control parameters in real time and generating a reference trajectory at the same time. The simulation experiment proves that compared with the traditional impedance control method, this method has faster force tracking speed and smaller force tracking error. It is a better force tracking control method.

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.

Practical Tracking Control of a Class of Uncertain Surface Vessels Under Weak Assumptions on Uncertainties and Reference Trajectories

2021 ◽  
Author(s):  
Jian Li ◽  
Wenqing Xu ◽  
Zhaojing Wu ◽  
Yungang Liu
Keyword(s):  
Tracking Control ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Unknown Parameters ◽  
Related Literature ◽  
Surface Vessels ◽  
Control Scheme ◽  
Reference Trajectories ◽  
Theoretical Results

Abstract This paper is devoted to the tracking control of a class of uncertain surface vessels. The main contributions focus on the considerable relaxation of the severe restrictions on system uncertainties and reference trajectory in the related literature. Specifically, all the system parameters are unknown and the disturbance is not necessarily to be differentiable in the paper, but either unknown parameters or disturbance is considered but the other one is excluded in the related literature, or both of them are considered but the disturbance must be continuously differentiable. Moreover, the reference trajectories in the related literature must be at least twice continuously differentiable and themselves as well as their time derivatives must be known for feedback, which are generalized to a more broad class ones that are unknown and only one time continuously differentiable in the paper. To solve the control problem, a novel practical tracking control scheme is presented by using backstepping scheme and adaptive technique, and in turn to derive an adaptive state-feedback controller which guarantees that all the states of the resulting closed-loop system are bounded while the tracking error arrives at and then stay within an arbitrary neighborhood of the origin. Finally, simulation is provided to validate the effectiveness of the proposed theoretical results.

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.

scholarly journals Optimal Clutch Pressure Control in Shifting Process of Automatic Transmission for Heavy-Duty Mining Trucks

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Heng Zhang ◽  
Xinxin Zhao ◽  
Jianning Sun
Keyword(s):  
Automatic Transmission ◽  
Pressure Control ◽  
Operating Conditions ◽  
Friction Loss ◽  
Extreme Condition ◽  
Reference Trajectory ◽  
Heavy Duty ◽  
Linear Quadratic ◽  
State Equations ◽  
Maximum Slope

The optimal control of automatic transmission plays an important role in the shifting smoothness and fuel economy of heavy-duty mining trucks. In this paper, a dynamic model of the powertrain system is built to study the clutch pressure control during the shifting process. A linear-quadratic optimal regulator is used to achieve the optimum control pressure of clutches, where shifting jerk and clutch friction loss are chosen to a form quadratic performance index function. Besides, a detailed solution of the linear-quadratic problem with the disturbance matrix in the state equations is provided. This paper also carries out a software simulation and verification of the normal condition (no load without slope) and the extreme condition (full load with maximum slope). Compared with the preset reference trajectory control, the simulation results show that the proposed optimal clutch pressure control can effectively reduce jerk and friction loss during the shifting process and has good robustness to different operating conditions.

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