In this abstract we introduce velocity control for our 2D dynamic walking robot Dribbel [1] (figure 1) and show that, by ‘closing the loop’, this automatically leads to increased robustness

Oort, G. van

Stramigioli, S.

English

In this abstract we introduce velocity control for our 2D dynamic walking robot Dribbel [1] (figure 1) and show that, by ‘closing the loop’, this automatically leads to increased robustness. Takuma and Hosoda [2] also have used active gait adaptation by using step-by-step feedback, but their research was largely based on experimental results, whereas this research is more theoretical

van Oort, Gijs

Stramigioli, Stefano

University of Twente Research Information

Velocity control of a 2D dynamic walking robotG. van OortImpact institute/University of Twenteg.vanoort@ewi.utwente.nlS. StramigioliImpact institute/University of Twentes.stramigioli@utwente.nl1 IntroductionIn this abstract we introduce velocity control for our 2Ddynamic walking robot Dribbel [1] (figure 1) and show that,by ‘closing the loop’, this automatically leads to increasedrobustness. Takuma and Hosoda [2] also have used activegait adaptation by using step-by-step feedback, but theirresearch was largely based on experimental results, whereasthis research is more theoretical.ϕ2ϕ1ϕ3stance leg swing legwalking directionsetpoint:θFigure 1: The dynamic walker Dribbel (left), a simulation model(middle) and the degrees of freedom (right). The hip isactuated; the knees are unactuated.2 The walking algorithm in DribbelThe control algorithm used in Dribbel and in the corre-sponding 20-sim simulations is very simple. As soon as theswing foot hits the ground, the (former) stance leg is swungforward. For this movement a very non-stiff P-controller isused in the hip. The setpoint θ can be varied.For each θ within a certain range, a limit cycle can be found,where the walker has a certain velocity (figure 2). Each limitcycle has a basin of attraction (denoted as BOA(θ)): the setof all states x =(ϕ1,ϕ2,ϕ3, ϕ̇1, ϕ̇2, ϕ̇3)T for which the walkerwill converge back to the limit cycle (i.e. it does not fall).3 Changing velocityChanging the velocity of the walker can simply be done bychanging the setpoint θ to a new value θnew. Given a certainstate x of the walker, it is interesting to know which valuesfor θnew can instantaneously be given without making thewalker fall. Theoretically, this can be formulated as follows:find the set Θ(x) = {θnew ∈ [0,π]|x ∈ BOA(θnew)} (1)such that, if the walker is in state x, choosing any θnew ∈Θ(x) will not make the walker fall (assuming no moredisturbances, of course). Similarly, a Θ(x∗) can be foundfor a reduced state x∗ = (ϕ2, ϕ̇1)T at the end of the step.The algorithm for changing velocity now works as follows.If the desired θnew is in Θ(x∗), directly change the setpoint0.2 0.25 0.3 0.35 0.40.20.220.240.260.280.30.32θ  [rad]velocity [m/s]Figure 2: The limit-cycle velocity of the walker for differentvalues of θ . This graph was obtained by simulation.to the desired value. If not, select a temporary θtemp ∈Θ(x∗)which is closest to θnew and wait a few steps before changingthe setpoint again.4 Improving robustnessA nice feature of this strategy is that it automaticallyincreases robustness. Assume that a disturbance puts thewalker in a state x∗dist . If x∗dist ∈ BOA(θ), it is no problem;the walker will automatically converge back to its limit cycleagain. If x∗dist 6∈ BOA(θ), then, using the same strategy, atemporary θtemp ∈ Θ(x∗dist) can be chosen which is close tothe original θ but does not make the walker fall.5 Implementation in DribbelA variant of the algorithm described above has already beenimplemented in Dribbel. As ϕ̇1 cannot be measured inDribbel (it lacks angular sensors in the feet), the set Θ isapproximated by a range [θmin,θmax] which is dependentonly on the walking velocity measured during the previousstep vlast-step = (2`sinϕ22 )/tstep (note that the step timetstep is related to the angular velocity of the stance legϕ̇1). Tests showed that with this algorithm it is indeedpossible to change the velocity without making the robotfall. Investigating how the robustness is affected is plannedfor the near future.AcknowledgementsThis research topic was initiated by Ester Guidi, whoalso implemented the velocity control algorith in Dribbel.Thanks also to Edwin Dertien for his help on the research.References[1] E. C. Dertien. “Realisation of an energy-efficientwalking robot”, Master’s thesis no. 022CE2005, Universityof Twente, June 2005.[2] T. Takuma, K. Hosoda. “Controlling the walkingperiod of a pneumatic muscle walker”, Int. J. RoboticResearch, Vol. 25, No. 9, p. 861-866, 2006.

Velocity control of a 2D dynamic walking robot

Controlling the walking period of a pneumatic muscle walker”,

Realisation of an energy-efﬁcient walking robot”, Master’s thesis no. 022CE2005,

http://purl.utwente.nl/publications/76369

Velocity control of a 2D dynamic walking robot

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