17. Multiobjective Control for Robot Telemanipulators

摘要

17.1 Introduction Teleoperation is the branch of robotics dedicated to manipulation in inaccessible environments. Such environments can be distant or hostile (space or nuclear) or can be at a different power scale (microsurgery or electronic assembly); see [80, 146]. A standard teleoperator system consists of a slave robot tracking a master robot via a bilateral link (the controller and the actuators). The master robot is manipulated by a human operator and the slave robot interacts with the environment (the load). Ensuring good tracking performance and maintaining system stability are the control objectives usually expressed in terms of network-based properties. It has been shown in [82] that passivity theory is useful to analyze the teleoperator stability for a wide range of operators and environments. A stability criterion was derived in [81] by verifying constraints on the scattering or admittance matrices of the teleoperator. A passivity approach for the design of a bilateral controller has been presented in [82]. A related method, based on optimization, is examined in [16, 435]. The use of convex optimization for a passive design is shown in [205]. A key point in the design of a bilateral controller is to ensure good trade-offs between the conflicting objectives of stability and performance. We propose a multiobjective design approach expressed in terms of linear matrix inequalities (LMIs). This formulation appears well suited for many control problems and especially for multiobjective ones; see [123, 365]. The present approach is close to the one discussed in [123] and generalizes the results obtained for linear time-invariant (LTI) systems subject to “structured” dissipative perturbations. The central idea is that a number of design specifications, such as robust (H2 norm) performance, robust input peak bound, etc., can be translated into LMI constraints associated with a nonconvex constraint of the form , where S, T are two (block-diagonal) matrix variables. Our problem can thus be solved using LMI optimization associated with an efficient cone complementarity linearization algorithm described in [128]. This makes our multiobjective robust design control problem amenable to an efficient numerical solution.