Abstract
In this paper, optimal cyclic reference trajectories aredesigned for three gaits of a quadruped robot, the curvet, theamble, and the trot, taking into account the actuatorscharacteristics. The gaits are composed of stance phases andinstantaneous double supports. The principle of virtual leg isused to obtain simpler dynamic model describing the motion ofthe quadruped. The impact phases are modeled by passive impactequations. For the curvet the step is composed of twodifferent half steps. For the amble and trot gaits twofollowing half steps are symmetrical.
The optimization problem is solved with an algebraicoptimization technique. The actuated joint evolution is chosenas a polynomial function of time. The coefficients of thepolynomial functions are optimization parameters. Thequadruped studied has non-actuated ankles. The kineticmomentum theorem permits to define the evolution of this non-actuated variable in function of the actuated variables. Twoenergetic criteria are defined: a torque cost and an energetic cost. The first is represented by the integral of the torquenorm and the second by the absolute value integral of theexternal forces work. The two criteria are calculated for adisplacement of one meter. During the optimization process,the constraints on the ground reactions, on the validity ofimpact, on the torques, on the joints velocities and on themotion velocity of the robot prototype are taken into account.Simulation results are presented for the three gaits. Allmotions are realistic. Curvet is the less efficient gait withrespect to the criteria studied. For slow motion, trot is themore efficient gait. But amble permits the fastest motion withthe same actuators.
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Muraro, A., Chevallereau, C. & Aoustin, Y. Optimal Trajectories for a Quadruped Robot with Trot, Amble and Curvet Gaits for Two Energetic Criteria. Multibody System Dynamics 9, 39–62 (2003). https://doi.org/10.1023/A:1021674132276
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DOI: https://doi.org/10.1023/A:1021674132276