Fast Convergent Gait Generation For Underactuated Spoked Walker With Torso

A rimless spoked wheel or simply rimless wheel (RW) is investigated as the most sim-plified model of passive dynamic walking. In McGeer’s early study on passive-dynamicwalkers,the stability of a RW was analyzed based on the return map. It was also clarified that apassive-dynamic gait of a RW is always one-periodand asymptotically stable because it au-tomatically achieves both constraint conditions for restored mechanical energy and impactposture. The constraint on impact posture is necessary to make the energy-loss coefcientconstant. The restored mechanical energy is always kept constant because the step lengthis constant. It is then shown that the kinetic energy immediately before impact convergesto the steady value. The generated passive-dynamic gait is obviously natural and energy-efcient.On the other hand, applications of inherent passive dynamics to efcient active walk-ing on level ground have been actively investigated. Active dynamic walkers with smallactuators are called limit cycle walkers in distinction from passive dynamic walkers, andthey can walk on level ground efciently exploiting their natural dynamics. During the lastdecade, many energy-efcient walkers have been developed and nowadays they are famil-iar in the field of robotic bipedal locomotion. The control design, however, has been acontinuous process of trial and error and the limit cycle stability remains unclear.Based on the previous research, fortunately, it has been clarified that a fast convergentgait can be generated by applying a simple output following control to a desired-time tra-jectory, and that a deadbeat gait can be generated by modifying the system parameters. Thedeadbeat gait is a walking gait whose discrete state error converges to zero only in one step.It can be said that the deadbeat gait is the optimal one in terms of the convergence speed.Such a fast convergent gait has a tremendous advantage in limit cycle walking on uneventerrain.Based on the observations, I propose a novel approach: continuous-time output dead-beat control (CODC) based on the discrete-time output deadbeat control (DODC). I in-troduce the model of an underactuated spoked walker with a torso that can exert the jointtorque between the stance leg and torso. The walker can walk forward by controlling thetorso and using the reaction moment. In this thesis, first, I propose CODC in which thecontrol input is defined as a linear function of time. By applying this method, the controloutput which is defined as the relative angle between the stance leg and torso is settled tozero and the mechanical energy lost at impact is successfully restored during the stancephases. Through analysis, I find that a deadbeat gait can be generated by changing thecontrol interval or desired settling time. Second, I investigate the properties of the gener-ated gait and compare the gait efciency with that generated by DODC through numerical simulations to prove the advantages of CODC. At last, I show some advantages in the gaitgenerated by CODC on uneven terrain and discuss the problems.