Discrete-Time Inverse Dynamics Control of Flexible Joint Robots

1992 ◽  
Vol 114 (2) ◽  
pp. 229-233 ◽  
Author(s):  
K. P. Jankowski ◽  
H. Van Brussel
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Inverse Dynamics ◽  
Differential Algebraic Equations ◽  
Control Methods ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Electromechanical Actuators ◽  
Flexible Joint Robots ◽  
Inverse Dynamics Control

This paper focuses on the problem of the application of inverse dynamics control methods to robots with flexible joints and electromechanical actuators. Due to drawbacks of the continuous-time inverse dynamics, discussed in the paper, a new control strategy in discrete-time is presented. The proposed control algorithm is based on numerical methods conceived for the solution of index-three systems of differential-algebraic equations. The method is computationally efficient and admits low sampling frequencies. The results of numerical experiments confirm the advantages of the designed control algorithm.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Multi-Splitting Waveform Relaxation Methods for Solving the Initial Value Problem of Linear Integral-Differential-Algebraic Equations

2011 ◽  
Vol 403-408 ◽  
pp. 1763-1766
Author(s):  
Xiao Lin Lin ◽  
Yuan Sang ◽  
Hong Wei ◽  
Li Ming Liu ◽  
Yu Mei Wang ◽  
...  
Keyword(s):  
Spectral Radius ◽  
Discrete Time ◽  
Initial Value Problem ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Initial Value ◽  
Relaxation Methods ◽  
Discrete Time Case ◽  
Linear Integral

We present the multi-splitting waveform relaxation (MSWR) methods for solving the initial value problem of linear integral-differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, a convergent condition is proposed for the MSWR method. Finally we discussed the convergent condition of discrete-time case of MSWR.

Modelica-Based Control of a Delta Robot

2020 ◽  
Author(s):  
Ahmed Okasha ◽  
Scott A. Bortoff
Keyword(s):  
Control Algorithm ◽  
Impedance Control ◽  
Experimental Testing ◽  
Differential Algebraic Equations ◽  
Control Algorithms ◽  
Algebraic Equations ◽  
Time Control ◽  
Delta Robot ◽  
And Control ◽  
Assembly Tasks

Abstract In this paper we derive a dynamic model of the delta robot and two formulations of the manipulator Jacobian that comprise a system of singularity-free, index-one differential algebraic equations that is well-suited for model-based control design and computer simulation. One of the Jacobians is intended for time-domain simulation, while the other is for use in discrete-time control algorithms. The model is well-posed and numerically well-conditioned throughout the workspace, including at kinematic singularities. We use the model to derive an approximate feedback linearizing control algorithm that can be used for both trajectory tracking and impedance control, enabling some assembly tasks involving contact and collisions. The model and control algorithms are realized in the open-source Modelica language, and a Modelica-based software architecture is described that allows for a seamless development process from mathematical derivation of control algorithms, to desktop simulation, and finally to laboratory-scale experimental testing without the need to recode any aspect of the control algorithm. Simulation and experimental results are provided.

Kinematic and Kinetic Derivatives in Multibody System Analysis

1997 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
System Analysis ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Efficient Computation ◽  
Computationally Efficient ◽  
Euler Parameters ◽  
Workspace Analysis ◽  
Dynamic Sensitivity Analysis ◽  
Derivatives Of

Abstract Methods and identities for computation of kinematic and kinetic derivatives required for a broad spectrum of multibody system analyses are presented. Analyses such as implicit numerical integration of the differential–algebraic equations of multibody dynamics, dynamic sensitivity analysis, and workspace analysis are shown to require computation of three derivatives of algebraic constraint functions and first derivatives of inertia and force expressions. Computationally efficient derivative calculation methods and associated identities are presented for Cartesian generalized coordinates, with Euler parameters for orientation. Results presented enable practical and efficient computation of all derivatives required in multibody mechanical system analysis.

Modeling, Realization, and Simulation of Thermo-Fluid Coupled Systems Using Singularly Perturbed Sliding Manifolds

2000 ◽  
Author(s):  
Brandon W. Gordon ◽  
Harry Asada
Keyword(s):  
State Space ◽  
Time Scale ◽  
Differential Algebraic Equations ◽  
Coupled Systems ◽  
Control Methods ◽  
Algebraic Equations ◽  
Singular Perturbation Method ◽  
New Approach ◽  
Sliding Control ◽  
Fluid Systems

Abstract A new approach based on sliding control is presented for modeling and simulation of thermo-fluid systems described by differential-algebraic equations (DAEs). The dynamics of thermo-fluid systems are often complicated by momentum interactions that occur on a time scale that is orders of magnitude faster than the time scale of interest. To address this problem the momentum equation is often modeled using algebraic steady state approximations. This will, in general, result in a model described by nonlinear DAEs for which few control methods are currently applicable. In this paper, the modeling problem is addressed using an approach that systematically constructs an explicit state space approximation of the DAEs. The state space model can in turn be used with existing control methods. This procedure, known as realization, is achieved by solving an associated nonlinear control problem by combining boundary layer sliding control with the singular perturbation method. The necessary criteria for key properties such as convergence are established. Further, the new approach is illustrated using a vapor compression cycle example. This demonstrates significant advantages over directly modeling momentum interactions.

Multibody Inverse Dynamics Using an Energy Preserving Direct Transcription Process

2003 ◽  
Author(s):  
Carlo L. Bottasso ◽  
Alessandro Croce
Keyword(s):  
Optimal Control Problems ◽  
Inverse Dynamics ◽  
Differential Algebraic Equations ◽  
Control Problems ◽  
Algebraic Equations ◽  
Dynamic Problems ◽  
Direct Transcription ◽  
Finite Dimensional ◽  
Transcription Process ◽  
Multibody Dynamic

We propose a procedure for the solution of inverse multibody dynamic problems, here intended as optimal control problems for dynamical systems governed by differential-algebraic equations. The numerical solution is obtained by a direct transcription process based on an energy preserving scheme that ensures nonlinear unconditional stability. The resulting finite-dimensional problem is solved by sequential quadratic programming. We test the proposed methodology with the help of representative examples.

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