Null-space-based optimal control reallocation for spacecraft stabilization under input saturation

2014 ◽  
Vol 29 (6) ◽  
pp. 705-724 ◽  
Author(s):  
Bo Li ◽  
Qinglei Hu ◽  
Juntong Qi
Keyword(s):  
Optimal Control ◽  
Null Space ◽  
Input Saturation ◽  
Spacecraft Stabilization

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics

2007 ◽  
Author(s):  
Sigrid Leyendecker ◽  
Sina Ober-Blo¨baum ◽  
Jerrold E. Marsden ◽  
Michael Ortiz
Keyword(s):  
Optimal Control ◽  
Rigid Body ◽  
Null Space ◽  
Numerical Dissipation ◽  
Discrete Version ◽  
Dynamical Equations ◽  
Time Stepping ◽  
Minimal Dimension ◽  
Energy And Momentum ◽  
External Forces

This paper formulates the dynamical equations of mechanics subject to holonomic constraints in terms of the states and controls using a constrained version of the Lagrange-d’Alembert principle. Based on a discrete version of this principle, a structure preserving time-stepping scheme is derived. It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. The resulting discrete optimal control algorithm is shown to have excellent energy and momentum properties, which are illustrated by two specific examples, namely reorientation and repositioning of a rigid body subject to external forces and the reorientation of a rigid body with internal momentum wheels.

A Successive Approximation Technique for Optimal Control Systems Subject to Input Saturation

1962 ◽  
Vol 84 (1) ◽  
pp. 33-37 ◽  
Author(s):  
Yu-Chi Ho
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Successive Approximation ◽  
Input Saturation ◽  
Computational Techniques ◽  
Approximation Technique

A class of problems that has received considerable attention in recent years from both control theorists and engineers is the following: Givenx˙=Fx+du,x(0)=cDetermine|u(t)|≤1suchthatx(T)=0andx(t)≠0for0≤t<TandwhereTisaminimum(P-1) A related and perhaps more practical class of problems can be stated as Givenx˙=Fx+du,x(0)=cDetermine|u(t)|≤1suchthat‖x(T)‖2PisaminimumforgivenT(P-2) Although a considerable amount of effort has been expended on (P-1), and to a lesser extent on (P-2), yet computational techniques which enable one to solve numerically the above problems are still lacking except in restricted cases [7, 8]. This paper presents such a technique which completely solves this problem by successive approximation. The convergence of this solution is proved, and it is shown to satisfy all known properties of the problems.

Sign in / Sign up

Export Citation Format

Share Document