OPTIMIZATION PROBLEMS OF CONTROLLED MULTIBODY SYSTEMS HAVING SPRING-DAMPER ACTUATORS* V. E. Berbyuk 1 and A. E. Boström 2 UDC 531.8+62-50 The optimal control of the motion of mechanical systems is studied. A characteristic feature of these systems is the presence of passive actuators (springs, dampers, etc.). Energy-optimal control laws and structural parameters of nonlinear spring–damper actuators are determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. As an example, a numerical solution is presented for the problem of designing an energy-optimal spring actuator for a robot manipulator of closed kinematic structure. Introduction. The necessity of improving the performance of modern machines and mechanisms brings forth the important problem of controlling the motion of mechanical systems in interrelation between the control laws and the typical features of the internal (proper) dynamics of these systems. The performance specifications of machines and mechanisms depend significantly on many factors such as the acting temperature field, friction in joints, damping properties of structural elements, etc. It is well known that springs and dampers are sometimes capable of improving the performance of mechanical systems. For example, spring–damper devices provide reliable vibroprotection for many machines and mechanisms. The effect of such devices on the dynamic behavior of an engineering system increases significantly in the presence of active (external) actuators [2, 5, 10, 14, 15]. In the present paper, we will concern ourselves with the synthesis of optimal control for mechanical systems with spring–damper actuators. Optimization problems for spring–damper actuators will be studied for a quite wide class of controllable mechanical systems. A functional quadratic in controls will play the role of an objective function. This functional is used to evaluate the energy consumed by electromechanical systems during motion [4, 7]. Energy-optimal control laws and structural parameters of nonlinear spring–damper actuators will be determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. Dynamic and control problems for mechanical systems simulating legged vehicles, robot manipulators, and other systems with spring–damper devices were earlier treated in [1–3, 5, 6, 8–11, 13–15]. 1. Formulation of the Problem. Let us consider a mechanical system with n degrees of freedom. Let the motion of the system be described by the equation A ( q 29 q .. + B ( q, q . 29 = C ( q 29 u ( t 29 , (1.1) where q = ( q 1 , q 2 , ..., q n 29 is the vector of generalized coordinates, u = ( u 1 , u 2 , ..., u m 29 is the vector of control actions (force and moments of forces) of actuators with external energy sources (for example, electric actuators), and A ( q 29 , B ( q, q . 29 , and C ( q 29 are given matrices. 1 Ya. S. Podstrigach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv, Ukraine. 2 Department of Mechanics of the Chalmers University of Technology, Göteborg, Sweden. Translated from Prikladnaya Mekhanika, Vol. 37, No. 7, pp. 115–120, July 2001. Original article submitted March 13, 2001. 1063-7095/01/3707-0935$25.00 ©2001 Plenum Publishing Corporation 935 International Applied Mechanics, Vol. 37, No. 7, 2001 * Read at the 20th International Congress of Theoretical and Applied Mechanics (August 27 – September 2, 2000, Chicago, USA). This is a complete report. The congress transactions include only an abstract.