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This paper presents algorithms for continuous-time quadratic optimization of impedance control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are found by solving an algebraic matrix equation. System stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. The solution results in design parameters in the form of square weighting matrices or impedance matrices as known from linear quadratic optimal control. The proposed optimal control is useful both for motion control and force control.>
Johansson et al. (Tue,) studied this question.