Asadpour, Masoud

Ijspeert, Auke Jan

Maye, Jerome

Moeckel, Rico

Sproewitz, Alexander

Infoscience - École polytechnique fédérale de Lausanne

Locomotion in Modular Robots based on Central Pattern GeneratorsA. Sproewitz, R. Moeckel, J. Maye, M. Asadpour, A. J. Ijspeert∗School of Computer and Communication ScienceEPFL - Ecole Polytechnique Fe´de´rale de LausanneStation 14, CH-1015 Lausanne, Switzerland{Alexander.Sproewitz, Jerome.Maye, Auke.Ijspeert}@epﬂ.ch, masoud.asadpour@gmail.com, moeckel@ini.phys.ethz.chAbstract We address the problem of learning to locomotein modular robotic systems, i.e. systems made from multiplehomogenous or heterogenous and highly autonomous mod-ules being assembled into a bigger robotic structure, otherthan monolithic robots (such as humanoid robot systems orpredeﬁned quadruped robots). We are particulary interestedin online learning of robust and adaptive locomotion for ar-bitrary robotic structures. We are using Central Pattern Gen-erators (an approach inspired by nature coping with redun-dancies in animal bodies and the easy generation of loco-motion patterns) in combination with a gradient-free opti-mization method (Powell’s method). We applied our ap-proach on three different robot conﬁgurations, interestinglocomotion modes are obtained after running the optimiza-tion for less than 60min. Our CPG model can be imple-mented easily in a distributed system among the moduleswith a low demand for computational power, it exhibits limitcycle behaviour (temporary perturbations are rapidly forgot-ten), the CPG produces smooth trajectories when control pa-rameters are abruptly changed, and it is robust against im-perfect communication between modules. As a testing andapplication platform we have developed the modular roboticsystem YaMoR. Among other key features it provides wire-less communication among the several YaMoR units basedon a specially developed Scatternet Protocol (SNP). As forthe future use as an autonomous reconﬁgurable system (Self-Reconﬁgurable Modular Robots) we are exploring reconﬁg-uration strategies based on a central approach using graphsignatures.Introduction As for all mobile robots, one of the key fea-tures for a modular robot is robust locomotion. Designingefﬁcient locomotion controllers for such modular systems ishowever a difﬁcult and unsolved problem. Their locomotioncontrol suffers from all the traditional difﬁculties of locomo-tion control in robots with multiple degrees of freedom. Ad-ditional difﬁculties arise due to their modular structure. (Self-reconﬁguring) modular robots are not necessarily optimizedfor a speciﬁc locomotion tasks (sub-optimal in terms of bal-ance and mass distribution, sufﬁcient actuation, alignmentand amount of degree of freedom). Therefore the controlof locomotion requires multi-dimensional coordinated rhyth-mic patterns that need to be correctly tuned such as to satisfy∗To whom correspondence should be addressed.θ i012r i012x i0 5 10 15 20 25 30 35 400pi2 piΔφiTime [s]Figure 1: Example of abrupt parameter changes in the CPG model.Output signals θi of the 5 oscillators (top). Amplitude state vari-ables ri (second from top). Offset state variables xi (third fromtop). Phase differences Δφi = φi+1 − φi between neighbor oscil-lators (bottom).multiple constraints: the capacity to generate forward motionpossibly with low energy consumption, without falling over,while adapting to possibly complex terrain (uneven ground,obstacles), and while allowing the modulation of speed anddirection.Locomotion control We propose a framework for learninglocomotion controllers based on two components: a centralpattern generator and a gradient-free optimization algorithm:Powell’s method (Press et al., 1994). Central pattern genera-tors (CPGs) are neural networks capable of producing coor-dinated patterns of rhythmic activity without any rhythmicinputs from sensory feedback or from higher control cen-ters (Delcomyn, 1980). We present a CPG based on a sys-tem of N coupled amplitude-controlled phase oscillators withN being the number of connected active modules per robotconﬁguration. See Fig. 1 for an example of 5 oscillators cou-pled in series, while control parameters are being abruptlychanged. Our CPG is implemented and tested on our YaMoRmodular robotic system. A YaMoR module has one actuateddegree of freedom (RC hobby servomotor, 1.1Nm torque),can be mechanically attached up to 5 other modules (using apin and groove system, see Fig. 2 for a 8-module assembly),186Figure 2: Quadruped robot assembly for 8 YaMoR modules (right)and its CPG structure (left). Solid lines show the bidirectional cou-plings between oscillators. The inner nodes (1, 3, 5 and 7) form aclosed loop of interoscillator couplings.has a self-sufﬁcient power supply for approx. 1.5 h and on-board computation abilities, and communicates wirelesslywith other modules via Bluetooth (Moeckel et al., 2006).Each module is programmed to run one nonlinear oscillatorto control the oscillations of its servomotor. Nonlinear oscil-lators are coupled together across modules using Bluetoothcommunication to obtain speciﬁc gaits, i.e. synchronized pat-terns of oscillations among modules. Different stable gaitscan be obtained by adjusting the parameters of the CPG thatdetermine the frequency, amplitude and phase lag of oscilla-tions.Online optimization CPGs are also a good substrate foronline optimization, a property that we focuse on in this para-graph. Indeed an optimization algorithm, in our case Pow-ell’s method, can run in parallel to the CPG and regularlyupdate its parameters via Bluetooth. Even so the updatesrepresenting abrupt changes, the CPG produces trajectoriesthat smoothly converge towards the new limit cycle after ashort transient period. Hence there is no need to stop or re-set the robot between iterations. We focus on online opti-mization, i.e. learning while moving other than using a sim-ulation or a model of our robot and the environment. As aﬁrst reason the transfer from a simulation/model to the realworld is often problematic due to difﬁculties in modelingcomplex environments (parameters for friction and contactmodels; inhomogenious friction in real world; backlash andoffsets in the motors; uncertainties in actuaction e.g. due todecreasing battery power). Second, it allows learning a lo-comotion gait for a new, previously unknown conﬁgurationsuch as after self-reconﬁguration or self-assembly. Third, thelocomotion gait may be continuously adapted to changes inthe robotic structure (e.g. because of the addition, removal,or failure of modules). Fourth, locomotion can be adaptedto changes in the environment. This work follows prelim-inary results in simulation with a slightly different type ofCPG that had shown the potential of the approach for mod-ular robotics (Marbach and Ijspeert, 2005). We applied ourcombined CPG/optimization method at three different robotstructures: a snake conﬁguration with two open parameters,a tripod robot with six and a quadruped assembly with 5 openoptimization parameters (see Fig. 2 for the CPG implemen-tation and the mechanical assembly of the quadruped robot).10 20 30 40 50 6000.511.522.533.544.5[rad]10 20 30 40 50 6000.511.522.533.54Time [min]Speed [cm/s]Figure 3: Powell’s optimization for the quadruped robot, with ﬁveopen parameters.We use as a cost function the speed of the robot, based on thedistance covered by locomotion for 8 s. Each evaluation ofthe optimization method takes in total 23 sec, we obtain inter-esting gaits (around 4.5 cm/s) for the quadruped robot within60min (Fig. 3). The two parameters for adjusting Powell’smethod are not specially ﬁne-tuned but being rather selectedto work for all our robot conﬁgurations.The above combined approach to generate optimized lo-comotion patterns on arbitrary modular robot conﬁgura-tions, using CPGs and a gradient-free optimization algorithmshows good results for a very small amount of evaluations(compared to e.g., stochastic optimization methods). Thisprovides a way for an online learning strategy, running CPGsand the optimization method in parallel on the real hardwareand in real time. We would like to extend this adaptive loco-motion learning to changing modular robot topologies (e.g.,simulated growing, shrinking, possibly removing and addinglimbs) and environmental situations.ReferencesDelcomyn, F. (1980). Neural basis for rhythmic behaviour inanimals. Science, 210:492–498.Marbach, D. and Ijspeert, A. J. (2005). Online optimizationof modular robot locomotion. In Proceedings of the IEEEInt. Conference on Mechatronics and Automation (ICMA2005), pages 248–253.Moeckel, R., Jaquier, C., Drapel, K., Dittrich, E., Upegui,A., and Ijspeert, A. J. (2006). Exploring adaptive locomo-tion with YaMoR, a novel autonomous modular robot withBluetooth interface. Industrial Robot, 33(4):285–290.Press, W., Teukolsky, S. A., Vetterling, W. T., and Flannery,B. P. (1994). Numerical recipes in C : the art of scientiﬁccomputing, 2nd edition. Cambridge University Press.287

Locomotion in modular robots based on central pattern generators

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Locomotion in modular robots based on central pattern generators

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