Quadratic Optimization of Motion Coordination and Control

This paper presents algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are found by solving an algebraic matrix equation. The system stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution results in natural design parameters in the form of square weighting matrices as known from linear quadratic optimal control The proposed optimal control is useful both for motion control, trajectory planning, and motion analysis.