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Controller design of cooperative manipulators using state-dependent Riccati equation

Published online by Cambridge University Press:  10 November 2017

Moharam Habibnejad Korayem
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology (IUST), 1684613114, Tehran, Iran. Email:
Saeed Rafee Nekoo*
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology (IUST), 1684613114, Tehran, Iran. Email:
*Corresponding author. E-mail:


This study examined the use of a state-dependent Riccati equation (SDRE) for controller design and analysis of cooperative manipulators. The connection of end-effectors when holding an object imports constraint and complexity into the problem. Optimal load distribution (OLD) was used to divide the load between arms using a desired rate and omitting Lagrange multipliers. General dynamic structure, OLD formulation, and controller design are presented for an arbitrary number of manipulators. State-dependent coefficient parameterizations for rigid and flexible joint manipulators assuming friction for joints of them were investigated by two methods: controlling each robot independently and an entire system of robots uniformly. The effectiveness of the method, a decrease in errors, and increased stability in motion were also observed. The increase in the number of manipulators greatly expanded the state vector of the system. The SDRE was able to address this by simulation of four arms, each one possessing seven degrees of freedom (DoF). Analyses of a practical model (Scout robot) consisting of two arms with three DoF were presented and the results for connected arms and free arms were compared. The experimental data validated the simulation results and indicated that cooperation definitely improves load-carrying capacity and precision of trajectory tracking.

Copyright © Cambridge University Press 2017 

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