Underactuated System

A systematic approach for designing analytical dynamics and servo
control of constrained mechanical systems is proposed. Fundamental
equation of constrained mechanical systems is first obtained
according to Udwadia-Kalaba approach which is applicable to
holonomic and nonholonomic constrained systems no matter whether
they satisfy the D'Alember's principle. The performance
specifications are modeled as servo constraints.
Constraint-following servo control is used to realize the servo
constraints. For this inverse dynamics control problem, the
determination of control inputs is based on the Moore-Penrose
generalized inverse to complete the specified motion. Second-order
constraints are used in the dynamics and servo control. Constraint
violation suppression methods can be adopted to eliminate constraint
drift in the numerical simulation. Furthermore, this proposed
approach is  applicable to not only fully actuated but also
underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.

Citation: Xiaoli Liu, Shengchao Zhen, Kang Huang, Han Zhao, Ye-Hwa Chen, Ke Shao. A systematic approach for designing analytical
dynamics and servo control of constrained mechanical systems. IEEE/CAA Journal of Automatica Sinica, 2015,  2(4): 382-393

Sloshing of liquid in a tank is important in several areas including launch vehicles carrying liquid fuel in space application, ships, and liquid cargo carriages. Hence modeling and characterization of nonlinear slosh dynamics is critical for study of dynamics of these systems. Additionally control of sloshing liquid offers a challenging problem of control of underactuated systems. To study slosh dynamics, develop useful identification schemes, and design and verify slosh control algorithms, a new 2DOF actuation slosh rig is reported in this paper considering the fact that most of the times the liquid tanks are subjected to linear as well as pitching excitation. The paper discusses mechatronic design and several advantages offered by the new design. Furthermore, a mathematical model of the rig is developed using Lagrange formulation assuming two-pendulum model for slosh. Slosh parameter identification with the rig is demonstrated in pitching and linear excitation cases. Nonlinear parameter identification schemes developed using simplified version of rig model are used for the purpose. Further results on compensation of slosh and rotary slosh phenomena are presented. Thus the proposed rig is ideal tool for study, identification, and control of slosh phenomena.

An interesting problem in robotics is to minimize the required time to force a manipulator to travel between two specific points (positioning time). In this paper a concurrent structure-control redesign approach is proposed in order to find the minimum positioning time of an underactuated robot manipulator, by considering a synergetic combination between the structural parameters and a bang–bang control law. The problem consists in finding the structural parameters of the system and the switching intervals of the bang–bang control that simultaneously minimize the positioning time, subject to the input constraint and the structural parameter constraint. The concurrent structure-control redesign approach is stated as a dynamic optimization problem (DOP). The projected gradient method is used to solve the DOP.The effectiveness of the proposed concurrent redesign approach is shown via simulation and experimental results on an underactuated system called the Pendubot.

1. THE MATCHING CONDITION This note presents an application of the method developed by Auckly, et al. (2000), to stabiliza-tion of a ball and beam system. The results are fully described in (Andreev, et al., (2000), Auckly, Kapitanski (2000), and Auckly, et al. (2000)). An ...

A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. In this paper, we describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we present the results from an experiment on a nonlinear ball and beam system.

This work is focused on the motion control of an underactuated brachiation robot with 3 links. We present the modeling of the dynamics of the robot and introduce the application of the model-based predictive control (MPC) using a linearized model of the system. The robot has 3 revolute joints but only one of them is actuated, i.e., the robot has less control inputs than degrees of freedom. The investigation of the MPC to control such a system is due to the fact that MPC is able to deal with constraints (state or input limitations) in a direct way, obtaining an optimal control law. Also, it is investigated the use of a linearized model for prediction of system state. Simulation results are shown for complete arm switching, as well as some directions for future developments

A recent approach to the control of underactuated systems is to look for control laws which will induce some speci3ed structure on the closed loop system. In this paper, we describe one matching condition and an approach for 3nding all control laws that 3t the condition. After an analysis of the resulting control laws for linear systems, we present the