Impedance control as an optimal control problem: a novel formulation of impedance controllers as a subcase of optimal co
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(2020) 42:513
TECHNICAL PAPER
Impedance control as an optimal control problem: a novel formulation of impedance controllers as a subcase of optimal control Guilherme Phillips Furtado1 · Pedro Parik Americano1 · Arturo Forner‑Cordero1 Received: 4 December 2019 / Accepted: 19 August 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract A formulation of impedance control for redundant manipulators is presented here as a particular case of an optimal control problem. This allows the design of an impedance controller that benefits from the stability and efficiency of an optimal controller. To circumvent the high computational costs of finding optimal controllers, a suboptimal feedback controller based on state-dependent Riccati equations (SDRE) is developed. This approach is compared with the quadratic programming (QP) formulation, commonly used to solve redundancy of robotic manipulators. Numerical simulations of a redundant planar four-DOF serial-link manipulator show that the SDRE controller offers superior performance over the QP one in terms of stability, performance and required control effort. Keywords Impedance control · Riccati equations · Optimal control · Quadratic programming · Redundant manipulator
1 Introduction This work presents a controller formulation, based on optimal control theory, to solve the impedance control problem of redundant robotic manipulators, which becomes more relevant as robots start to interact more closely with humans. As proposed by [21], impedance control aims at regulating the dynamic behavior of a system as it interacts with the environment. Unlike pure force or position control, impedance control maintains a prescribed relationship between interaction forces and displacements resulting from this interaction. A well-designed dynamical behavior enables, effectively, simultaneous control of position and contact force of an end-effector, as it interacts with an unknown environment. The formulation of impedance control as a particular case of an optimal control problem has the advantage of generating an efficient controller according to multiple,
Technical Editor: Victor Juliano De Negri, D.Eng. G. P. Furtado Passed away January 2020. * Arturo Forner‑Cordero [email protected]; [email protected] 1
Biomechatronics Lab, Mechatronics Department, Escola Politecnica da Universidade de Sao Paulo, Sao Paulo, SP 05508‑030, Brazil
conflicting optimization criteria while handling mixed input/ state constraints and guaranteeing stability. The impedance control strategy has been applied to a wide range of engineering problems that involve unknown or intermittent contact between a robot and the environment. For example, in teleoperation, impedance control can be used to design the robot compliance as well as a haptic interface used by a human operator [18, 32, 49]. Another application of impedance control is the simulation of virtual dynamical interactions, such as in the design of interactive virtual environments with haptic interfaces [1] or healthcare a
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