Stabilization of the position of a Lagrangian system with elastic elements and bounded control, with and without measurement of velocities

✍ Scribed by I.V. Burkov; L.B. Freidovich

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 574 KB
• Volume: 61
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(97)00055-5

✦ Synopsis

R is required to positio~l a Lagrang~ system whose free and controllable degrees of freedom are elastically linked. The equations of motion of such systems describe, in particular, the dynamics of a robot manipulator with elastic joints. The proposed control laws enable restrictions ,an the value of the control impulse to be taken into account. In particular, attention is given to the situation in which the velocities are not access~le to measurement. The analysis of the proposed control laws is based on Lyapunov's direct method or, more: specifically, on the Baxbashin-Krasovskii theorem on asymptotic stability in the large. The proof uses an original method to verify that an auxiliary non-linear function, analogous to the total mechanical energy of a system, closed by a control law, is positive-definite. @ 1997 Elsevier Science Ltd. All fights reserved.

l. STATEMENT OF THE PROBLEM

Consider a Lagrangian dynamical system with Lagrangian L = 1 (qtrD(q ! )ql + il~Jq2 + (q! -q2 )r K(ql _ q2)) + U(q! )