The dynamics of legged locomotion in heterogeneous terrain: universality in scattering and sensitivity to initial conditions Feifei Qian and Daniel I. Goldman Georgia Institute of Technology Atlanta, Georgia 30332–0250 Abstract —Nat ural substrate s are often compos ed of parti cu- lat es of var yin g siz e, fr om fine sand to peb ble s and bou lde rs. Robot locomotion on such heterog eneou s substrates is compli- cat ed in par t due to lar ge forc e and kin ema tic fluc tua tions intr oduc ed by heter ogene ities . T o syste matic ally expl ore how het erogeneity aff ect s loc omotion, we stu dy the movement ofa hexape dal robot ( 15 cm, 150 g) in a trac kway fil le d wi th ∼1 mm “sand”, wit h a lar ger con ve x “bould er” of var iou s shape and roughness embedded within. We investigate how the pr esence of the boulde r aff ect s the robot ’s trajec tor y . T o do so we de vel op a ful ly- automated terrain cr eat ion sys tem, the SCA TTER (Systematic Creation of Arbitrary Ter rain and T esting of Explor atory Robots), to contr ol the init ial conditi ons of the substrate, including sand compaction, boulder distribution, and substrate inclination. Analysis of the robot’s trajectory indicates that the interaction with a boulder can be modeled as a scatterer with attractive and repulsive features. Depending on the contact position on the boulder, the robot will be scattered to different directions after the interaction. The trajectory of an individual interaction depends sensitively on the initial conditions, but re- markably this dependence of scattering angle upon initial contact locat ion is univ ersa l over a wide range of bould er propert ies. For a larger heterogeneous field with multiple “scatterers”, the traje ctory of the robot can be estimated using a super posit ion of the sca tte ri ng angles from eac h sca tte re r . Thi s scatte rin g super posit ion can be applied to a vari ety of compl ex terrains , including heterogeneities of different geometry, orientation, and texture. Our results can aid in development of both deterministic and statistical descriptions of robot locomotion, control and path planning in complex terrain. I. I NTRODUCTION Roc ky , loo se substrates are common in en vir onments tha t explo rat ory rob ots must tra ver se; suc h ter rai ns can con tai n gra nul ar med ia (GM) wit h par tic le siz es spa nni ng many orders of magni tude . When robotic loco moto rs travel acr oss the se “flo wab le” typ es of het ero gen eous ter rai n, the y exhib it characteristic failure modes (sl ips , uns tab le foot -hol ds , impa ss able ba rr ie rs , cour se de vi at ions , or limb/t rea d fluidiz ati on of a thin lay er of smaller par ticles) which sign ifican tly aff ect robo t stab ilit y , maneuver abil ity and power consumpti on. One of the maj or cha lle nge s in creat ing the next gener atio n of mobi le robo ts is expa nding the sco pe of ter ramech ani cs [1] [2] fro m lar ge tra cke d and tr ea ded ve hi cles on homogeneous gr ound to ar bi tr ar il y shaped and ac tuat ed locomotors mo vi ng on and wi thin comple x het ero gen eou s terrestrial substrates, to create a “ter radyn amic s” [3] (in anal ogy to hydr o and aero dynamics whic h pr ovide predictive po wer for aquatic and ae ri al vehi cles ) of loco moti on on heter ogene ous groun d. Howe ver, in typical heterogeneous environments, the force fluctuations intr oduced by heterogeneities (gra vels, rocks, boul ders , etc.) dur ing intru sio n and dra g can be lar ge, which mak es the applicability of conti nuum terr amechani cs [1][ 2] uncle ar. Currently, most terrestrial vehicles (including mobile robots) are test ed on subst rates made of standardi zed homog enous media (e.g. Ottowa sand [4], lunar simulants [5]), while robot locomotion on hete rogen eous gran ular grou nd is rela tiv ely unexplored. Mo del l ing and con tr ol l in g rob ot lo comot ion on heteroge neous gr anul ar te rr ai n re quir es fundamenta l unde rs ta nding of the comple x inte ra ct ions betwee n the rob ot and the gro und . Thi s int era cti on can be esp eci all y complicated when obst acles possess mobilit y rela tiv e to the sub str ate und ern eat h (e. g., bou lde rs/ roc ks can rotate, til t, shift on or ev en sink int o the fine san d). Multi ple types ofint era cti ons – rob ot wit h the fine san d [3] , rob ot wit h the mult i-sh aped bould ers/ rocks , as well as boul ders/ rocks with the fine sand – must be considered, and the mobility of the boulde rs/ roc ks can dynamica lly cha nge the ter rai n pro file during the interaction. Studying the response of a locomotor on het ero gen eous gra nul ar ter rai n wil l gen era te a bet ter understan ding of such inte ract ions, and this unde rsta nding can pro vid e a pre dic ti ve gui dan ce in na vig ati on pla nni ng. Most traditional navigation planning methods involve finding a coll is ion fr ee pa th, whic h re quir es the robot to av oi d obstacles. For example, the potential field method (PFM) [6] treats obst acle s as repul siv e pote ntials that repel the robot . Thi s is le git imate for mos t whe ele d/t rea ded rob ots whi ch must circumvent obstacle s, but for leg ged robo ts, traver sing obstacles by stepping over or upon them [7] can be another opt ion . All owing rob ots to interact wit h obs tac les [8], or even man ipu lat e the loc omo tio n en vir onment [9] , cou ld signi ficant ly expa nd viab le expl orat ion spac e for obst acle - fill ed en vir onment s. Suc h adv anc es in rob ot mob ili ty wil l al so re quir e a stat is ti ca l te rr adynamic s fr amewor k for locomotion and control, in which deterministic understanding of rob ot- het ero gen eit y int era cti ons can be use d as inp uts. A sta ti sti cal terradyna mic s wil l allow rob ots to evalu ate obstacle traversability and predict the probability of outcomes
