scholarly journals A Novel Dual Quaternion Based Cost Effcient Recursive Newton-Euler Inverse Dynamics Algorithm

2019 ◽  
Vol 1 (2) ◽  
pp. 144-168
Author(s):  
Cristiana Miranda de Farias
Keyword(s):  
Feedback Linearization ◽  
Inverse Dynamics ◽  
Joint Space ◽  
Linearization Method ◽  
Torque Control ◽  
Dual Quaternion ◽  
Serial Manipulators ◽  
Dual Quaternions ◽  
Forward Kinematic ◽  
Computed Torque

In this paper, the well known recursive Newton-Euler inverse dynamics algorithm for serial manipulators is reformulated into the context of the algebra of Dual Quaternions. Here we structure the forward kinematic description with screws and line displacements rather than the well established Denavit-Hartemberg parameters, thus accounting better efficiency, compactness and simpler dynamical models. We also present here the closed solution for the dqRNEA, and to do so we formalize some of the algebra for dual quaternion-vectors and dual quaternion-matrices. With a closed formulation of the dqRNEA we also create a dual quaternion based formulation for the computed torque control, a feedback linearization method for controlling a serial manipulator's torques in the joint space. Finally, a cost analysis of the main Dual Quaternions operations and of the Newton-Euler inverse dynamics algorithm as a whole is made and compared with other results in the literature.

Robust Framework for the Computed Torque Control of Nondeterministic Multibody Dynamic Systems

2016 ◽  
Author(s):  
Sahand Sabet ◽  
Mohammad Poursina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Feedback Linearization ◽  
Torque Control ◽  
Control Law ◽  
Mathematical Framework ◽  
Computed Torque Control ◽  
Highly Nonlinear ◽  
Multibody Problems ◽  
Computed Torque

Considering uncertainty is inarguably a crucial aspect of dynamic analysis, design, and control of a mechanical system. When it comes to multibody problems, the effect of uncertainty in the system’s parameters and excitations becomes even more significant due to the accumulation of inaccuracies. For this reason, this paper presents a detailed research on the use of the Polynomial Chaos Expansion (PCE) method for the control of nondeterministic multibody systems. PCE is essentially a way to compactly represent random variables. In this scheme, each stochastic response output and random input is projected onto the space of appropriate independent orthogonal polynomial basis functions. In the field of robotics, a required task is to force robotic arms to follow designated paths. Controlling such systems usually leads to difficulties since the dynamic equations of multibody problems are highly nonlinear. Computed Torque Control Law (CTCL) is able to overcome these difficulties by using feedback linearization to evaluate the required torque/force at any time to make the system follow a trajectory. In this paper, a mathematical framework is introduced to apply the Computed Torque Control Law to a multibody system with uncertainty. Surprisingly, it is shown that using this control scheme, uncertainty in geometry does not affect the closed-loop equations of controlled systems. Both the intrusive PCE method and the Monte Carlo approach are used to control a fully actuated two-link planar elbow arm where each link is required to follow a specified path. Lastly, a comparison of the time efficiency and accuracy between the traditionally used Monte Carlo method and the intrusive PCE is presented. The results indicate that the intrusive PCE approach can provide better accuracy with much less computation time than the Monte Carlo method.

scholarly journals COMPUTED TORQUE CONTROL FOR A SPATIAL DISORIENTATION TRAINER

2020 ◽  
Vol 18 (2) ◽  
pp. 269
Author(s):  
Jelena Vidaković ◽  
Vladimir Kvrgić ◽  
Mihailo Lazarević ◽  
Pavle Stepanić
Keyword(s):  
Control System ◽  
Robot Control ◽  
Inverse Dynamics ◽  
Control Method ◽  
Robot Manipulator ◽  
Training System ◽  
Torque Control ◽  
Spatial Disorientation ◽  
Computed Torque Control ◽  
Computed Torque

A development of a robot control system is a highly complex task due to nonlinear dynamic coupling between the robot links. Advanced robot control strategies often entail difficulties in implementation, and prospective benefits of their application need to be analyzed using simulation techniques. Computed torque control (CTC) is a feedforward control method used for tracking of robot’s time-varying trajectories in the presence of varying loads. For the implementation of CTC, the inverse dynamics model of the robot manipulator has to be developed. In this paper, the addition of CTC compensator to the feedback controller is considered for a Spatial disorientation trainer (SDT). This pilot training system is modeled as a 4DoF robot manipulator with revolute joints. For the designed mechanical structure, chosen actuators and considered motion of the SDT, CTC-based control system performance is compared with the traditional speed PI controller using the realistic simulation model. The simulation results, which showed significant improvement in the trajectory tracking for the designed SDT, can be used for the control system design purpose as well as within mechanical design verification.

scholarly journals Task-Space Admittance Controller with Adaptive Inertia Matrix Conditioning

2021 ◽  
Vol 101 (2) ◽  
Author(s):  
Mariana de Paula Assis Fonseca ◽  
Bruno Vilhena Adorno ◽  
Philippe Fraisse
Keyword(s):  
Feedback Linearization ◽  
Inverse Dynamics ◽  
Poor Performance ◽  
Joint Space ◽  
Robot Dynamics ◽  
Reference Trajectory ◽  
Task Space ◽  
End Effector ◽  
Inertia Matrix ◽  
Matrix Conditioning

AbstractWhenrobots physically interact with the environment, compliant behaviors should be imposed to prevent damages to all entities involved in the interaction. Moreover, during physical interactions, appropriate pose controllers are usually based on the robot dynamics, in which the ill-conditioning of the joint-space inertia matrix may lead to poor performance or even instability. When the control is not precise, large interaction forces may appear due to disturbed end-effector poses, resulting in unsafe interactions. To overcome these problems, we propose a task-space admittance controller in which the inertia matrix conditioning is adapted online. To this end, the control architecture consists of an admittance controller in the outer loop, which changes the reference trajectory to the robot end-effector to achieve a desired compliant behavior; and an adaptive inertia matrix conditioning controller in the inner loop to track this trajectory and improve the closed-loop performance. We evaluated the proposed architecture on a KUKA LWR4+ robot and compared it, via rigorous statistical analyses, to an architecture in which the proposed inner motion controller was replaced by two widely used ones. The admittance controller with adaptive inertia conditioning presents better performance than with a controller based on the inverse dynamics with feedback linearization, and similar results when compared to the PID controller with gravity compensation in the inner loop.

A Survey on Control of Parallel Manipulator

2007 ◽  
Vol 339 ◽  
pp. 307-313 ◽  
Author(s):  
J.F. He ◽  
H.Z. Jiang ◽  
D.C. Cong ◽  
Zheng Mao Ye ◽  
Jun Wei Han
Keyword(s):  
Control Strategies ◽  
Parallel Manipulators ◽  
Physical Structure ◽  
Extensive Study ◽  
Torque Control ◽  
Serial Manipulators ◽  
Advanced Control ◽  
And Performance ◽  
Computed Torque ◽  
Structure Properties

Based on extensive study on literatures of control of parallel manipulators and serial manipulators, control strategies such as computed torque control, PD+ control, PD with feedforward compensation, nonlinear adaptive control are classified into two categories: model-based control and performance-based control. Besides, as advanced control strategies, robust control and passivity-based control for the parallel manipulators are also introduced. Comparative study in view of computation burden and tracking performance are performed. It turned out that the physical structure properties of parallel manipulators’ dynamics are similar with that of serial ones, and this constitutes a common foundation for the two kinds of manipulators to develop together that control design of parallel manipulators can start with ever established control methods of serial manipulators.

Predictive Trajectory Tracking Algorithm of Underactuated Systems Based On the Calculus of Variations

2021 ◽  
Author(s):  
Bálint Bodor ◽  
Ambrus Zelei ◽  
László Bencsik
Keyword(s):  
Inverse Dynamics ◽  
Numerical Study ◽  
Tracking Error ◽  
Torque Control ◽  
Underactuated Systems ◽  
Inverse Kinematics Problem ◽  
Predictive Controller ◽  
Servo Constraints ◽  
The Stability ◽  
Computed Torque

Abstract The tracking control of underactuated systems is a challenging problem due to the structural differences compared to fully actuated systems. Contrarily to fully actuated systems, resolving the inverse kinematics problem of underactuated systems is not possible independently from the dynamic equations. Instead, the inverse dynamics must be addressed. It is common to extend the computed torque control (CTC) technique with servo constraints. Besides the CTC's clearness, the stability of the system cannot be always guaranteed. A novel predictive controller (PC) is presented in this paper. Our PC applies the variational principle to design the motion of the system in order to achieve a stable motion with the lowest possible tracking error. To demonstrate the applicability and the performance of the PC method, a numerical study is presented for a planar manipulator resulting in about 20% RMS error compared to the CTC method from the literature.

Computed Torque Control of Articulated Multibody Systems in the Generalized Divide and Conquer Algorithm Framework

2015 ◽  
Author(s):  
Cameron Kingsley ◽  
Mohammad Poursina
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Torque Control ◽  
Divide And Conquer ◽  
Controlled System ◽  
Divide And Conquer Algorithm ◽  
Computed Torque Control ◽  
And Control ◽  
Computed Torque

An extension to the Generalized-Divide-and-Conquer Algorithm (GDCA) is presented in this paper in conjunction with the Computed-Torque-Control-Law (CTCL) to model and control fully actuated multibody systems. CTCL uses the inverse dynamics to provide control inputs to the system while, the dynamics of the system must be formed and solved in each iteration. Herein, the GDCA is extended to form and solve the inverse dynamics to find control torques. Further, this method is also extended to efficiently solve the equations of motion of the controlled system. This significantly reduces the complexity of modeling, simulating, and controlling the fully actuated multibody systems to O(n) or O(logn) operations in each iteration in the serial and parallel implementations, respectively.

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