【正文】
n the machine is in teleoperated or autonomous needs appropriate reactivity from the machine,the operator must receive visual feedback as quickly as possible in order to check if the action he planned and ordered is correctly executed by the autonomous mode,the more rapidly the machine reacts to a sudden event,the more chances it has to adapt to the changing in gait switching can be improved in different ways:by shortening the response time to supervision mands or by reducing the total time of the transition response time to supervisory signals represents in fact a possible delay in the case where a required transition cannot occur at the current timethe mechanics response time of the actuators is not considered the mode of control described in this paper,emphasis is made on reducing the duration of the transition ,since the control from low to high levels is to be executed onboard,putation times are to be considered walking control presented allows efficient implementation with very low putation times. The paper is divided in four first one is devoted to the improved design of the forward crawl gait thanks to sideways second section describes turning motions and the particular turn around the next section deals with the last section results are presented. sideways crawl gaitSimple crawl gait The first stage of study consisted in testing the simple crawl gait on the experimental Sony quadruped helps to bee aware of the real problems of defined by Mc Ghee[1],the crawl gait is a regular symmetric term 39。regular39。 means that each leg reproduces the same trajectory cycle with a phase term 39。symmetric,means that trajectories of opposite legs(assuming a rectangular shape for the body)are halfa cycle out of phase. Hence the phase difference between consecutive legs on one side determines entirely the sequence of legs in the creeping figure(2),the general crawl gait is represented using leg state diagrams,higher values refer to the air phase of the legs when they are moving forward to reach their next foothold to begin a new traction (3a)and figure(3b)represent the successive transitions in the crawl the cycle always three legs remain on the ground,the period of time called 39。duty factor39。 P is the fraction of cycle relative to the standing the crawl the maximum value for P is 3/4,see figure(2). If up and down moving times of the legs are neglected,the body velocity VG can be expressed as: where v is the leg swinging velocity. In this paper the study of the crawl focuses on gaits ,which allows the robot to reach a maximal speed while keeping three legs on the ground at all times. Looking at figures(3a)and(3b)the four changes in the set of the three supporting legs are changes can be partitioned into two pairs or first class regroups the two transitions where the take off of a rear leg occurs immediately after the landing of the diagonally opposite front other class contains the remaining leg changes where the takeoff of a front leg occurs immediately after the landing of the rear leg located on the same is clear that the first class can suffer losses of balance as the COG is situated just at the frontier of the stability polygon,see figure(3).However the center must absolutely remain just above this front ierline,for instance if there is some deviation between the COG and the geometric center,+the risk for the robot to tip over is increased as the COG can go out of the current stability polygon some time or solve this problem it is possible to introduce aside ways motion of crawl gait with sideways motion The idea of sideways motion is not new,it has been introduced by Hirose[6]to study continuous generation of gaits from crawl to the trot sideways motion is determined according to dynamics considerations aimingat neutralizing the overturning momentum due to gravity around the diagonal supporting line[ crawl can not be termed a quasistatic gait since there are two transitions where the vertical projection of the COG is theoretically on the diagonal edge of the support the strategy of the trot gait can not be applied to this case since there is theoretically nooverturning gravity momentum..Amplitude of sideways motion Considering a sine sideways motion of G,denoted by a(t),the problem is to determine its amplitude a: T being the cycle practice there are always differences between the theoretical and the real positions of the center of mass at the instants of transitions of class 1,and these differences can lead to instabilities when the projection of the COG is outside the support of such an instability should be kept to a achieve this the machine must have enough kinetic energy at the time of the transition in order that the COG joins the moving diagonal support line without yielding to the overturning momentum of gravity acceleration,see figure(4).Here a deviation along yaxis,6,between the real and theoretical centers of mass is simulated as first class transition we call the instant of transition time and tl the instant when G joins the diagonal support line in Go,the maximal kinetic energy between these two moments of time is: with v(tl)=O in the worst is the mass of the dh,where d is the distance to the diagonal support line at to(fig.(4)),and h the height of G,the work performed by the overturning gravity momentum is approximately equal to: If kinetic energy is spent to counteract the work developed by gravity,it es: where p is the angle of incline of the diagonal support line,the deviation between the current position of G and G0,T the cycle period,and VGy the velocity ponent along the direction of motion(yaxis).This formula cannot been utilized to determine exact practical values of fact 6,VG and p can only be approximated in practice as they are subjected to this equation shows that if p is increased,amplitu