Beck, Fabian

Loeffl, Florian Christoph

Werner, Alexander

Institute of Transport Research:Publications

Fitting Task Specific Elastic Potential for Robotic LegsFlorian Loeffl1, Fabian Beck1, and Alexander Werner1,2I. INTRODUCTIONIt is a common understanding that efficient legged lo-comotion requires energy to be stored and released in acyclic manner. Equipping mechanical leg systems with springsprovides this functionality and forms an oscillatory system.It is a design goal to fit this oscillatory behavior to thelocomotion task, which is only in few special cases realizablein an exact manner [1]. Abate et al. present a concept ofexploiting some kind of mechanical gearing to map a certainstiffness into task space [2]. In contrast, our concept aims todesign an elastic potential supporting the whole task executionin an optimal way. Additionally, our concept can also beapplied to systems with kinematic redundancies, which cannotbe addressed by pure mapping approaches. Limitations ofthe actuation dynamics caused by low impedance actuation[3], need only be accepted for the task degrees of freedom(DoF). Being only marginally involved during task execution,nullspace DoF allow for high impedance actuation. Thisenhances the versatility of the system.This work presents an approach that can:• Relax the actuator requirement during nominal task exe-cution, by an optimal fit of the elastic properties.• Tune the intrinsic oscillatory behavior to obtain a behav-ior similar to the task, by adapting the potential.• Enhance the disturbance rejection capability, by allowinghigher torque bandwidth actuation for certain degrees offreedom.• Provide an intuitive interpretation of the effect of partic-ular elastic elements in the design.• Be employed on every cyclic task of articulated robots.II. CONCEPTOur goal is to design an elastic potential, that generatestorques and forces , as similar as possible to the total taskforces while moving along the intended task trajectory. Bydoing so we gain the work done by physical elastic springsand thus lower the work necessary done by the actuators.We assume the cyclic task to be a one dimensional curve injoint space. Under some conditions, this allows to identifyrelationships of the motions of each joint and its predeces-sor along the kinematic chain. Approximating these relativemotions by linear regression we generate a similar motionbased on a chain of fixed ratio biarticular couplings. AddingThis project has received funding from the European Research Council(ERC) under the European Union’s Horizon 2020 research and innovationprogramme with the grant agreement No 819358, NatDyReL.1 Institute for Robotics and Mechatronics, German Aerospace Center(DLR), Germany.2 Department of Electrical and Computer Engineering, University ofWaterloo, Canada.E-mail address: florian.loeffl@dlr.dey = -1,6566x - 7,9969 15284154-38 -33 -28 -23 -18Knee torque τ 2 / [Nm] Hip torque τ1 / [Nm] Hip torque vs. knee torque Fig. 1: Fit of the task spring coupling ratio of -1.66:1 fromthe knee torque τ2 over hip torque τ1 plot.an actuator on each of those couplings spans our approximatednullspace. In the same manner the loads in the joints can betreated, distributing the forces of one single elastic potentialover all involved joints.III. ALGORITHMThe process can be summarized into four steps:1) Prepare and examine the input data from physical orsimulation experiments regarding periodicity and uni-formity.2) Fit displacement variables to generate forces along thetask trajectory from the analysis of relative torque tra-jectories.3) Generate displacement domains orthogonal to the taskdirections to stabilize the system pose based on the linearregression fit of relative displacement trajectories.4) Optimize the stiffness parameters for the task execution.Figure 1 shows one of the fits, done in step 2. This fit derivesthe torque ratio of 1.66 between hip and knee task forces fora squat motion on C-Runner.REFERENCES[1] D. Lakatos, W. Friedl, and A. Albu-Schäffer, “Eigenmodes of nonlineardynamics: Definition, existence, and embodiment into legged robots withelastic elements,” IEEE Robotics and Automation Letters, vol. 2, no. 2,pp. 1062–1069, April 2017.[2] A. Abate, R. L. Hatton, and J. Hurst, “Passive-dynamic leg designfor agile robots,” in IEEE International Conference on Robotics andAutomation (ICRA), May 2015, pp. 4519–4524.[3] G. A. Pratt and M. M. Williamson, “Series elastic actuators,” in Intelli-gent Robots and Systems 95.’Human Robot Interaction and CooperativeRobots’, Proceedings. IEEE/RSJ International Conference on, vol. 1.IEEE, 1995, pp. 399–406.

Fitting Task Specific Elastic Potential for Robotic Legs

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Fitting Task Specific Elastic Potential for Robotic Legs

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