On the Solution of Inverse Dynamics and Trajectory Optimization Problems for Multibody Systems

2004 ◽  
Vol 11 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Carlo L. Bottasso ◽  
Alessandro Croce ◽  
Luca Ghezzi ◽  
Paolo Faure
Keyword(s):  
Trajectory Optimization ◽  
Multibody Systems ◽  
Inverse Dynamics ◽  
Optimization Problems

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.

scholarly journals A trajectory design method for RLV via artificialmemory-principle optimization

2018 ◽  
Vol 189 ◽  
pp. 10019
Author(s):  
Hao Li ◽  
Changzhu Wei
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Memory Cell ◽  
Optimization Method ◽  
Alternative Solution ◽  
Trajectory Design ◽  
Memory State ◽  
Artificial Memory

A trajectory optimization method for RLV based on artificial memory principles is proposed. Firstly the optimization problem is modelled in Euclidean space. Then in order to solve the complicated optimization problem of RLV in entry phase, Artificial-memory-principle optimization (AMPO) is introduced. AMPO is inspired by memory principles, in which a memory cell consists the whole information of an alternative solution. The information includes solution state and memory state. The former is an evolutional alternative solution, the latter indicates the state type of memory cell: temporary, short-and long-term. In the evolution of optimization, AMPO makes a various search (stimulus) to ensure adaptability, if the stimulus is good, memory state will turn temporary to short-term, even long-term, otherwise it not. Finally, simulation of different methods is carried out respectively. Results show that the method based on AMPO has better performance and high convergence speed when solving complicated optimization problems of RLV.

DirCol5i: Trajectory Optimization for Problems With High-Order Derivatives

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Matthew P. Kelly
Keyword(s):  
Nonlinear System ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
High Order ◽  
Robot Arm ◽  
Minimum Jerk ◽  
Higher Derivatives ◽  
A Chain ◽  
Fifth Order ◽  
Reference Trajectories

In this technical brief, we focus on solving trajectory optimization problems that have nonlinear system dynamics and that include high-order derivatives in the objective function. This type of problem comes up in robotics—for example, when computing minimum-snap reference trajectories for a quadrotor or computing minimum-jerk trajectories for a robot arm. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses the fifth-order splines and analytic differentiation to compute higher-derivatives, rather than using a chain-integrator as would be required by traditional methods. We compare DirCol5i to traditional transcription methods. Although it is slower for some simple optimization problems, when solving problems with high-order derivatives DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.

Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Original System ◽  
Parent Body ◽  
Divide And Conquer ◽  
Loop Control ◽  
Generalized Coordinates ◽  
Divide And Conquer Algorithm ◽  
Generalized Force ◽  
New Formulation

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Sign in / Sign up

Export Citation Format

Share Document