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J. Human. Robot."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>This paper proposes a nonlinear optimal control approach for the three-link biped robot. In this humanoid robot there is actuation only in the two legs while the third link which is the robot\u2019s torso is unactuated. Due to nonlinearities and the unactuated torso in the robot\u2019s dynamics, the treatment of the stabilization and trajectories tracking problem is a non-trivial task. To solve the associated nonlinear optimal control problem, the state-space model of the three-link biped robot undergoes approximate linearization based on Taylor series expansion and the associated Jacobian matrices. For the linearized state-space model of the biped robot a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller\u2019s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. 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