Towad a Vitual Neuomuscula Contol fo Robust Walking in Bipedal Robots Zachay Batts, Seungmoon Song, and Hatmut Geye Abstact Walking contolles fo bipedal obots have not yet eached human levels of obustness in locomotion. Imitating the human moto contol might be an altenative stategy fo geneating obust locomotion in obots. We seek to contol bipedal obots with a specific neuomuscula human walking model poposed peviously. Hee, we pesent a vitual neuomuscula contolle, VNMC, that emulates this neuomuscula model to geneate desied moto toques fo a bipedal obot. We test the VNMC on a high-fidelity simulation of the ATRIAS bipedal obot constained to the sagittal plane. We optimize the contol paametes to toleate maximum gound-height changes, which esulted in ATRIAS walking on a teain with up to ±7 cm height changes. We futhe evaluate the obustness of the optimized contolle to extenal and intenal distubances. The optimized VNMC adapts to 9% of andom teains with gound-height changes up to ± cm. It endues 95% of ±3 Ns hoizontal pushes on the tunk, and 9% of 8 Ns backwad and 4 Ns fowad impulses on the swing foot thoughout the gait cycle. Futhemoe, the VNMC is esilient to modeling eos and senso noise much lage than the equivalent uncetainties in the eal obot. The esults suggest VNMC as a potential altenative to geneate obust locomotion in bipedal obots. I. INTRODUCTION State of at locomotion contolles enable bipedal obots to walk outside the laboatoy envionment [1] [4]. A typical contolle takes high-level goals fom a footstep planne, uses a simple dynamics model to plan the coesponding cente of mass (COM) tajectoies, and geneates taget joint toques of the full obot that ealize these tajectoies [5]. Recent implementations of this appoach eplan the footsteps online to eact to unexpected distubances [1], o account fo the full dynamics of the obot to calculate desied joint toques [3], [6]. Othe contolles employ moe heuistic policies to ovecome unexpected distubances. Fo example, intuitionbased policies that adjust the step length, leg thust, and tunk lean have demonstated stable locomotion [], [7]. Despite these advances, walking contolles have not yet eached the obustness of human contol in locomotion, which makes it difficult to use bipedal obots in scenaios such as escuing lives fom natual and man-made disastes. An altenative contol stategy is to imitate the human contol of locomotion. Although the human contol is not fully undestood, vaious neuomuscula models have been poposed to explain fundamental contol mechanisms of human locomotion [8] [1]. Fo instance, it has been demonstated in physics simulations that neual contolles, consist- This wok is suppoted in pat by the DARPA M3 pogam (W91CRB- 11-1-). Z. Batts, S. Song, and H. Geye ae with the Robotics Institute, Canegie Mellon Univesity, 5 Fobes Avenue, Pittsbugh, PA 1513, USA. {zbatts,smsong,hgeye}@cmu.edu neual contolle Fig. 1. Vitual neuomuscula contol fo bipedal obot locomotion. An emulated neuomuscula model is mapped to a obot topology (ATRIAS pictued) to geneate desied moto toques. ing of cental patten geneatos and muscle eflex modules, can geneate stable 3-D walking [9], [1]. Coesponding bioinspied contolles have been developed to geneate walking in humanoid obots [13] [16]. They demonstate stable walking with toleance to modeate distubances and ae often used fo miniatue humanoid obots [15], [16]. Howeve, the existing bioinspied walking contolles do not demonstate locomotion that is moe obust than the afoementioned obotic contolles. Hee, we seek to contol a bipedal obot ATRIAS with a specific neuomuscula human walking model we peviously poposed [1] (Fig. 1). This model can geneate obust 3-D locomotion on ough teain (unexpected gound-height changes of ±1 cm), esist extenal pushes (8 86 Ns), and geneate divese locomotion behavios in simulation. Howeve, it is unclea whethe the obust locomotion obseved in the simulation tansfes to the physical obot, since the dynamics of ATRIAS ae significantly diffeent fom human dynamics, and senso noise and actuato satuation may limit pefomance. This pape epots on peliminay wok of adapting the neuomuscula model as a contolle fo ATRIAS in simulation. The simulation platfom models the existing expeimental testbed of ATRIAS constained to the sagittal plane by a boom (Sec. II). We develop a vitual neuomuscula contolle, VNMC, that emulates the neuomuscula model and maps the model to the ATRIAS geomety to geneate desied moto toques (Sec. III-A). We optimize the contol paametes fo maximum gound-height changes (Sec. III- B), which esults in ATRIAS walking on a teain with ±7 cm height changes. We analyze this walking behavio
TABLE I S EGMENT PROPERTIES OF ATRIAS AND A HUMAN MODEL [1] tunk uppe leg lowe leg foot COM mass length mass length mass length height mass to hip ATRIAS human model 1 35 57.9 53.5 5 46 1.1 8.5 5 46 1. 3.5 8 1.5 (unit: cm, kg) and the obustness of the contolle to extenal and intenal distubances (Sec. IV). The optimized VNMC toleates 9% of the teains with gound-height changes up to ± cm. It endues 95% of ±3 Ns hoizontal pushes on the tunk, and 9% of 8 Ns backwad and 4 Ns fowad impulses on the swing foot though out the gait cycle. In addition, the VNMC is esilient to modeling eos and senso noise much lage than the coesponding uncetainties in the eal obot. The esults suggest that the VNMC is a potential altenative to geneate obust locomotion in bipedal obots. We discuss the limitations of the cuent implementation of VNMC and potential outcomes of ou wok (Sec. V). II. ATRIAS SIMULATION PLATFORM ATRIAS is a human-size (1-m leg length and 63-kg body weight) bipedal obot that is designed to concentate the mass at the tunk [17], which esults in segment dynamics diffeent than those of humans (Table I). Each of ATRIAS legs is a lightweight fou-ba linkage that makes point contact with the gound. Two seies elastic actuatos (SEAs) located at each hip joint dive the fou-ba linkage in the sagittal plan. A thid gea-moto contols the leg in the fontal plane, which can be used fo 3-D locomotion. In this study, we use a high-fidelity simulation of the ATRIAS platfom constained in the sagittal plane, which was developed and tested in a pevious study [18] (Fig., Matlab Simulink/SimMechanics R14b). The ATRIAS model has 1 intenal degees of feedom (4 fo the fou-ba linkages, 4 fo the SEAs, and fo the fontal plane motos). In addition, a boom constains ATRIAS to a cicula tack, while the tunk is allowed to pitch. The fontal plane motos ae egulated to keep both legs in the sagittal plane. Futhemoe, the simulation includes the detailed SEA dynamics and contol (max toque: 35 Nm), and dynamic gound contact models that captue stick-slip fiction. While we simulate the continuous dynamics of the physical system with a vaiable time-step solve (ode45, elative eo toleance: 1e-3, absolute eo toleance 1e-4), the contol loop uns discetely at 1 khz to match the contol fequency of the actual obot. The simulation includes the encodes used to estimate the position and oientation of the tunk, intenal joint angles, and SEA moto toques. III. VIRTUAL NEUROMUSCULAR CONTROL A. Vitual Neuomuscula Contolle The vitual neuomuscula contolle (VNMC) simulates a neuomuscula model to deive desied joint toques of the ATRIAS obot fo walking (Fig. 3). The obot s Fig.. Simulation of the -D expeimental testbed of ATRIAS. The top ight pictue shows the actual testbed of ATRIAS constained to a cicula tack by a boom. We use a high-fidelity simulation of this testbed to investigate vitual neuomuscula contol. tunk lean, fowad velocity, joint angles and joint toques (θ, v, ϕ, τ ) ae mapped to vitual measuements equied to simulate the neuomuscula model, which ae the tunk lean, fowad velocity, joint angles, loading foce on the legs, and the foot-contact infomation (θv, vv, ϕv, fv, cv ). The neuomuscula model outputs vitual joint toques (τv ) that ae mapped to desied obot joint toques (τ ), which ae then tacked by the SEA contolle. The neuomuscula model of the VNMC is adapted fom the sagittal hip and knee components of the human contol model in [1]. The model includes a skeletal system, muscletendon units, and a neual cicuity. The skeletal system is a kinematic chain that compises the tunk, thigh and shank segments connected by the hip and knee joints. The skeletal system is synchonized with ATRIAS, in that the tunks, hips and the feet ae collocated. Monoaticula and biaticula muscles geneate vitual toques aound the hip and knee joints. The neual cicuits contol the vitual muscles by geneating muscle stimulations based on the neual sensoy data fom the musculoskeletal system. We teat the neuomuscula model as a black box that geneates vitual joint toques based on the vitual measuements, τv = τv (θv, vv, ϕv, fv, cv ). (See [1] fo details on the contol cicuity.) The emaining pat of the VNMC convets the sensoy data of the obot to the vitual measuements, Φϕ: (θ, v, ϕ, τ ) (θv, vv, ϕv, fv, cv ), and the vitual toques to desied obot joint toques, Φτ : τv τ. The tunk lean and the fowad velocity of the vitual skeleton ae identical to that of ATRIAS, {θv, vv } = {θ, v }. The emaining measuements ae conveted though geometic tansfomations. The joint angles of the skeletal system, R L1 L, ae mapped fom ϕv = ϕr1 v, ϕv, ϕv, ϕv the joint anr L1 L gles of the obot, ϕ = ϕr1. Fo instance,, ϕ, ϕ, ϕ the kinematic elation fo the joints of the ight (R) leg is 1 R R ϕr1 π + ϕr1 (1) v = + ϕ + ϕv R l ϕ ϕr1 1 () cos ϕr = sin v lv
encodes neual sensing SEA dynamics neual contolle SEA contolle muscle stimulation ATRIAS neuomuscula model vitual neuomuscula contolle Fig. 3. Vitual neuomuscula contolle on ATRIAS. The encodes on the ATRIAS model measue the states of the obot used by the VNMC. The SEA contolle tacks desied toques to dive the ATRIAS model. The desied toques ae geneated by VNMC, which simulates a neuomuscula model that is mapped to the obot geomety. whee l and l v ae the segment lengths (the thigh and shank ae equal in length) of the obot and vitual legs, espectively. We model mechanical limits of ATRIAS that pevent the ight hand side of Eq. () fom eaching singulaity. (All the mappings ae the same fo the left leg.) The loads on the legs, f v = ( f R v, f L ) v, ae the components of the gound eaction foces that act in the diection fom the feet to the hips. These ae estimated, assuming quasi-static equilibium, fom the obot joint toques, τ = ( ) τ R1, τ R, τ L1, τ L, as τ R1 f R v = l sin τ R ( ϕ R ϕr1 ). (3) The boolean vecto, c v = ( ) c R v, c L v, indicates whethe the legs ae in contact with the gound. We assume a contact is made if the leg foce (f R v o f L v ) exceeds 5% of body-weight. Finally, the vitual joint toques, τ v = ( ) τv R1, τv R, τv L1, τv L, ae mapped to ) desied obot actuato toques, ˆτ = R1 (ˆτ, ˆτ R, ˆτ L1, ˆτ L, as [ˆτ R1 using the Jacobian, ˆτ R ] T = Φ T τ [τv R1, τv R ] T (4) [ 1+k Φ τ = k 1 k k between vitual and obot joint velocities with ( ) ϕ R l sin ϕr1 k = ). (6) l v cos The vitual knee angles (ϕ R v ( ϕ R v ] (5) and ϕv L ) ae satuated at 179 deg to avoid singulaity in Eq. (6), and the desied toques (ˆτ ) ae satuated at the maximum actuato toques, ±35 Nm. B. Optimization of the VNMC paametes We optimize the contol paametes, p R n (n = 5), of the black box neuomuscula model to geneate obust walking. Specifically, we simulate ATRIAS walking on a cicula tack with one-mete-long flat gound tiles of andomly vaying heights and use optimization to find the lagest height diffeence h max that ATRIAS successfully taveses. Fo that pupose, we constuct the cost function as { d tgt d walk, if d walk < d tgt J(p, h max ) =, (7) h max, othewise whee d tgt is a taget tavel distance (d tgt = 3 m.5 laps), and d walk is the distance the model walks befoe falling. The cost function was designed consideing two possible simulation outcomes: falling and completing the couse. Fist, if the model fails to each the taget distance (d walk < d tgt ), the cost deceases the futhe the model walks. Second, if the model successfully taveses the tack (d walk d tgt ), the cost deceases as the lagest gound-height change ( h max ) inceases, which is also an optimization paamete. The initial seed paametes fo optimization wee hand-tuned on flat teain (not pesented in this pape). We use the covaiance matix adaptation evolution stategy [19] to optimize the contol paametes fo minimum cost. IV. RESULTS A. Optimized Walking fo Rough Teain With the optimized VNMC, ATRIAS can walk on a teain with maximum height diffeences of ±7 cm (see accompanying video). Figue 4 shows kinematic and kinetic data fo 13 seconds of this walking behavio, duing which the obot taveses the maximum height changes. The obot gains and loses fowad velocity (v ) as it descends and ascends the tiles, espectively. The tunk lean (θ ) and step length, which ae ecognized as impotant factos in contolling walking speed [], [1], show a close tend with the fowad velocity. Duing the fist few steps, vetical gound eaction foces (GRFs) show the chaacteistic double-hump patten of human walking. In the late steps, the GRFs show chatte, which seems to emege fom the vibation of the swing leg. If the swing leg oscillates, the stance contol attempts to
-7cm +7cm 1 1 14 16 18 t (sec) [ms -1 ] 4 [deg].9 step length [m].4 GRF [BW] -1 18 [deg] 9 5 [deg] 135 35 [Nm] -35 35 [Nm] -35 Fig. 4. Kinematic and kinetic data while walking on ough teain. The top panel shows snapshots pojected to a -D plane of ATRIAS evey 1 second walking on a ± 7cm teain. The panels below show the fowad velocity v, tunk lean θ, step length, ight leg gound eaction foces (gay: left leg; scaled to body weight (BW)), ight leg joint angles ϕ R1 and ϕ R (gay: left leg), and ight leg desied joint toques ˆτ R1 and ˆτ R (magenta: SEA toques). Stance phases of the ight leg ae maked by gay backgound. compensate it by poducing simila oscillating toques that popagate to the GRFs. Since this undesied behavio is not obseved in the oiginal human neuomuscula model, it may oiginate in the SEA dynamics and the discetized contolle. Nevetheless, VNMC adapts to the unobseved teain by modulating the fowad velocity, step lengths, gait peiods, and joint tajectoies. B. Robustness Test of the Optimized VNMC We evaluate the obustness of the optimized VNMC by simulating a vaiety of distubances that ae typical in a ealwold envionment, including gound-height distubances and extenal pushes. In addition, we examine the contolle toleance to modeling eo and senso noise. We assess the obustness of the contolle against goundheight distubances by evaluating the success ate of tavesing sets of andom teains with diffeent levels of difficulty. We test on 1 sets of teains with vaying gound-height. Each set consists of 1 andom 3-mete-long teains with a common maximum gound-height change ( h max ) that anges fom ±1 cm to ±1 cm acoss the sets. We count the
tials [%] 1 8 6 4 success backwad fall fowad fall (a) Success ate fo tunk impulses impulse magnitude [Ns] 1 5-5 1 success ate [%] 4 6 8 1 [cm] -1 Fig. 5. Robustness to ough teain. Shown ae the pecentage of success (black line), backwad fall (ed dashed line), and fowad fall (blue dashed line) in walking tials ove sets of teains with maximum gound-height diffeences h max of ±1 cm to ±1 cm. tials fo which ATRIAS successfully taveses the teains of each set (Fig. 5). The success ate is ove 9% up to ± cm teains, significantly deceases to 5% at ±3 cm, and is zeo fo all the teains ove ±7 cm. Up to ±7 cm teains, the obot tends to fall backwad often losing fowad momentum while walking up the teains. We speculate that the absence of the ankle joint, which povides lage fowad populsion in the oiginal human model [1], limits the obustness against gound distubances. In addition, the oiginal neuomuscula model modulates the tunk lean to geneate additional populsion [1]; howeve, the COM of ATRIAS tunk is close to the hip, which attenuates the effect of this stategy. Fo teains with lage height changes ( h max 8 cm), the popotion of falling fowad inceases. This is because ATRIAS moe often kicks the vetical face of the tiles, which causes the obot to tip fowad. In addition to studying ough gound locomotion, we test the contolle against extenal pushes to the tunk and the swing foot while walking on flat gound. Fist, we apply constant hoizontal foces anging fom [ 1, 1] N fo 1 ms on the COM of the tunk at diffeent phases of the gait cycle. We test fo diffeent stides and evaluate the success ate (Fig. 6-A). The contolle endues about 95% of ±3 Ns pushes thoughout the gait cycle. In geneal, it can withstand lage backwad pushes than fowad pushes. It can also toleate lage pushes aound heel stike, which is when the kinetic enegy of the obot is maximal duing the gait cycle (efe to v data in Fig. 4). Second, we conduct a simila expeiment on the swing foot with foces anging fom [ 6, 6] N (Fig. 6-B). The obot can esist about 9% of the impulses of 8 Ns and +4 Ns. The contolle is moe obust to fowad impulses duing ealy swing, since the swing foot acceleates fowad at this phase in nomal walking. To backwad impulses, it is most obust duing midswing when the fowad velocity of the foot is maximal. The left leg is moe sensitive than the ight leg to backwad pushes duing late swing. This asymmety is likely due to the cicula tack, which aleady foces the left leg (the inne (b) Success ate fo swing foot impulses impulse magnitude [Ns] 6 4 - -4-6 left swing ight swing 4 6 8 1 gait cycle [%] Fig. 6. Robustness to extenal pushes. (a) Success ate fo hoizontal impulses to the tunk COM fo the ange of [ 1, 1] Ns with 1 Ns esolution fo evey 1% of the gait cycle. (b) Success ate fo hoizontal impulses to the swing foot in the ange of [ 6, 6] Ns with 4 Ns esolution. leg) to swing less than the ight in nominal walking. We also evaluate the esilience of the optimized VNMC against intenal distubances: modeling eos and senso noise (Table II). Fo modeling eos, we find the ange of tunk and leg inetias and the SEA sping popeties fo which the obot can maintain walking. In geneal, VNMC is esilient to modeling eos. Fo example, it can withstand thee times inceased leg inetia and five times stiffe SEA spings. Based on a pevious study with the simulation and hadwae of ATRIAS [18], the uncetainties in the actual dynamic popeties ae much less than the modeling eos VNMC toleates. Similaly, we add Gaussian noise to the encode signals until the obot falls down, and VNMC withstands senso noise much lage than that expected in the actual obot. The obot walks with up to σ =.1 deg of noise in all ten encodes that measue intenal DOFs, which is much lage ( 1e6) than the eo of the 3-bit encodes on the obot. The VNMC is insensitive to the global fame measuements used in the contol, which ae the tunk lean (θ ) and fowad velocity (v ) (Table II). This indicates that the contolle does not equie high-fidelity acceleometes and gyoscopes to measue this data. On the othe hand, it implies that the optimized VNMC does not
TABLE II SENSITIVITY TO MODELING ERRORS AND SENSOR NOISE. DYNAMIC PROPERTIES ARE THE MASS AND INERTIA OF THE TRUNK AND LEGS, AND THE ELASTICITY AND DAMPING OF THE SEA SPRINGS. dynamic popeties min... max noise max σ tunk 8%... 14% ϕ.1 deg leg 3%... 33% θ 7.5 deg SEA sping 8%... 56% v 1 ms 1 fully use the functionalities of the oiginal neuomuscula contol, which stabilizes the tunk and modulates the foot placement based on these measuements. Pehaps the VNMC would be moe obust by taking full advantage of these contol functionalities. V. SUMMARY AND FUTURE DIRECTION In this pape, we poposed a vitual neuomuscula contolle, VNMC, to geneate obust walking fo the bipedal obot ATRIAS. VNMC simulates a human neuomuscula model, and maps the model to ATRIAS to geneate desied joint toques. We optimized the contol paametes to toleate maximum gound-height changes, which esulted in ATRIAS walking on a ±7 cm teain. We tested the esulting contolle against extenal and intenal distubances. Using the contolle, ATRIAS toleates about 9% of the teains with gound-height changes of ± cm. It endues 95% of ±3 Ns hoizontal pushes on the tunk, and 9% of 8 Ns backwad and 4 Ns fowad impulses on the swing foot thoughout the gait cycle. In addition, VNMC is esilient to modeling eos and senso noise much lage than the equivalent uncetainties in the eal obot. The esults suggest VNMC as a potential altenative to geneate obust locomotion in bipedal obots. The cuent VNMC is less obust than the oiginal neuomuscula human model, which toleates ove ± cm in -D []. We speculate that thee main easons account fo this eduction in pefomance. Fist, the segment popeties of the obot ae diffeent fom that of humans. Fo example, ATRIAS does not have feet which geneate lage populsion in the human model (Sec. IV-B). Second, the SEA dynamics and the discetized contol loop seem to cause undesied high fequency oscillations in the walking motion (Sec. IV-A). 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