Balance Control in Interactive Motion

Transcription

1 Balance Control n Interactve Moton by Yuanfeng Zhu Drected By Professor Mchael Neff & Professor Bernd Hamann

2 What s Interactve Moton? Fghtng Game Acton Game A knd of acton occurs as two or more objects have an effect upon one another. Sports Game Move

3 Why Balance Control? Key problem: to generate varous character responsve moton wth physcs-realty feature. Keep standng, Jumpng back, Steppng back, Rollng back, Or just Fallng down. Balance control s an area of nterest n several felds ncludng humanod robotcs and character anmaton. In these felds, where the style of the moton s as mportant as ts effectveness [Zordan et al TOG 009].

4 Prevous Achevement on Balance Control Balance Problems set of estng technques to solve balance problem solved wth one or both of the followng ways: 1. Data-drven smulaton : producng hgh qualty motons of human characters. [Popovć et al EUROGRAPHICS 008] not easly generalzable and rely heavly on data for realsm. [Zordan TOG 009] we choose. Physcs-based smulaton: automatcally consstent wth the envronment; [Popovć et al EUROGRAPHICS 008] requre sophstcated controllers, balance problem. [Zordan et al TOG 009] often unnatural because they are dffcult to control. [Popovć et al EUROGRAPHICS 008] track reference for more natural moton. Moton controller: a strategy to drve the body parts to move to the desred pose wth/wthout dsturbance and requrements of tmng, balance and other user-requred constrants.

5 Physcs-based Balance Control Zordan et al [SCA 00]: Moton capture-drven smulatons that ht and react Desgn a control systems: Trackng MoCap data to accomplsh specfed tasks; Balance control: COM tracks COM trajectory of moton data by a PD controller whch generates vrtual force that s then decomposed to drve lower body for balanced standng. Bong moton by trackng MoCap data

6 Physcs-based Balance Control Jorvan Popovc et al [SCA 007]: Mult-objectve Control wth Frctonal Contacts Standng controller wth mult-objectves: wthn optmzaton framework. Balance control by makng CM near the center of feet support whle tryng to reach mult-objectves as near as possble. The weght of a reachng objectve s gradually ncreased, pushng the character to a more precarous stance.

7 Physcs-based Balance Control Vctor Zordan et al[tog 009]: Momentum Control for Balance Standng Controller wth large dsturbances: response to large dsturbances wthn a optmzaton-based framework Control balance by trackng CP and the CM of moton data smultaneously Response followng a dsturbance on head

8 Physcs-based Balance Control KangKang Yn et al[siggraph 007]: SIMBICON: Smple Bped Locomoton Control Robust Walkng Controller wth large dsturbances: Real-tme response to large dsturbances Control balance by protectve steps based on CM poston and velocty Trackng reference Response followng a dsturbance on upper body

9 Motvaton Estng: a branch of physcs-based methods to control moton balance whch support nteracton wth envronment for varous human moton, ncludng balanced standng, walkng, runnng... Not Estng: In the full-dynamc smulaton envronment After a large dsturbance to character, For any moton controller, proposed novel features over prevous work: 1. Fast judge whether current controller can acheve objectve moton pose wth eact tmng requrement wthout tme-consumng forward dynamc smulaton.. Precsely predct whether current controller can generate a balance moton. Ultmate goal of our system wth above novel features Once dsturbance happens user nput desred acton pose wth eact tmng (optonal ) and moton style (optonal ) requrement Our system fast generates a best-ft (reasonable and feasble) control soluton to acheve the user-defned moton goal whle keepng balance. Potentally appled our system nto fghtng acton desgn for game and move

10 System Overvew Start Select a moton controller from moton database Desgn ntal & desred poses wth/wthout tmng nformaton Smulate moton wth default controller parameters. Montor nteracton from user Yes No Catch an nteracton? Yes End Judge whether workable? (objectve pose & not fall) No Most mportant component Solve controller parameters by optmzaton framework wth constrants (acheve objectve pose, keep balance, PD-controller gan boundary ) Resume smulaton wth solved controller parameters

11 Optmzaton framework Gven an estng controller and the attack Objectve: mnmze total energy when the moton s (nearly) back to the desred poston. Satsfy Constrants: 1. Requre moton style (optonal): A. Under-damped(by default) B. Crtcal C. Over-damped Oscllaton D. other styles. Fast judge: objectve pose s achevable wth {eact tme(optonal)} 1 st Lyapunov-functon Constrant 3. Judge current balance state and predct future nd Lyapunov-functon Constrant How Lyapunov Functon works?

12 Introducton of Lyapunov Functon Wdely used to analyze stablty n dynamc system, especally robotcs area such as: 1. Analyze stablty of a robot controller reachng a target whle avodng obstacles wth lnear-velocty-based Lyapunov functon. [Benzerrouk et al. IEEE Workshop on Robotcs and Intellgent Transportaton System, RITS 010]. Moton stablty of a robot controller to travel through a door wth lnear-and -angular-velocty-based Lyapunov functon. [Akanyet et al. Journal Robotcs and Autonomous Systems 010] However, not appled to computer anmaton area yet. Advantage: Gven a dsturbance, a reasonable controller C, a desred poston Pd a constructed Lyapunov Functon L based on C & Pd. Once L confrms stable at balance posture=> C workable n whole progress. Dffculty: construct a workng Lyapunov functon? =>No standard way.

13 Defnton of Lyapunov functon

14 Determne Stablty by Lyapunov Functon ontroller C How to buld a V()? Dfferent moton=> dfferent control strateges dfferent V()

15 The 1 st Lyapunov Constran CL1 Fast Judge : whether current controller can acheve objectve moton pose wthout forward dynamc smulaton. In dynamc smulaton, Prevous optmzaton framework need background forward dynamc smulaton to test each canddate control soluton to confrm whether to acheve the moton goal Acheve desred pose Suffcng tmng requrement (optonal) Keep balance Drawback: forward dynamc smulaton tme-consumng Our optmzaton framework wthcl1: Overcome drawback: flter canddate solutons workable to acheve the desred pose by a knematcal way, and avod unneeded dynamc smulaton tests.

16 The 1 st Lyapunov Constran CL1 Fast Judge : whether current controller can acheve objectve moton pose, wth eact tmng and moton style requrement, wthout forward dynamc smulaton. Gven a PD-controller C: When X: jont angle under-damped oscllator. Construct Lyapunov functon: If 4I * kp kd * kd 0 V ( X ) L 1 0 => C acheve P d I * X kp*( X X d ) kd * X t / dt X ( t) Ae sn(t / T 0) X X d L1 w * Sgh ( t)* I * 0 A desred pose wth jont angle set Xd={Xd} X d Punch P d C C C t -1 t 0 t d t e

17 The 1 st Lyapunov Constran CL1 Fast Judge : whether current controller can acheve objectve moton pose wthout forward dynamc smulaton Demo to demonstrate advantage of Cl1

18 The 1 st Lyapunov Constran CL1 Fast Judge: whether current controller can acheve objectve moton pose wthout forward dynamc smulaton. However CL1 gnores eternal forces (gravty and ground reacton) CL1 cannot predct Controller C generate balanced lateral moton CL s proposed to predct balance state of the future moton Punch P 0 t 0 C C C t 1 t t 3

19 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. Prevous work to predct balance state, several steps of forward smulaton s sampled to confrm current balance state and then guess the future. Tradtonal (COM-based) method: COM ϵ FSA(Foot support area) Accuracy lmted by samplng range [t0,t] Y X Z After seconds samplng of COM poston usng forward dynamc smulaton, COM method predct t balanced wrongly.

20 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. A novel Constrant CL based on a constructed Lyapunov Functon L Note Lyapunov Functon can predct dynamc stablty 1) L s workable. predct balance ) 1 st Oscllaton not fall Z Component of COM poston Desred poston X* Tme(s) balanced standng

21 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. Math descrpton of CL Goal to predct not fall 1 L s workable. 1st Oscllaton not fall 1 L ( ) ma L ( ) 1 L ( ) ma( m 1 Where c Kp =1 As X; = As Z 0 Knetc Energy Potental Energy L 1 ( ) mc Kp ( ) ( * ( )*( * )) 0 * ) d COM FSA (Foot Support Area) when 1 st Oscllaton

22 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. New Practcal Fndng A balance controller an oscllaton style of CM moton around the desred poston n the local coordnate system of the foot support area (FSA) untl stop. Z Component of COM poston Z Component of COM poston CM moton curve balanced standng under attack Z Component of COM poston Tme(s) Tme(s) Tme(s) balanced jumpng balanced walkng

23 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. Assume: Smulate oscllaton-style of CM moton by Vrtual Non-lnear PD-controller m c Kp ) ( Physcs Eplanaton: 1) Jont torque=> drag to desred poston ( * ) Kd ( )* ) Gravty torque=>make body part fallng around jont Mass poston Tme(s) Moton curve of jont PD-controller

24 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. Smplfy the nd Lyapunov Constrant: By transformaton wth To much smpler descrpton: Based on the observaton: Balanced moton=>damped COM oscllaton=> Therefore 0 ) ( ma ) ( ma ) ( 1 1 Kd L L To demonstrate: )) )( ( ma( ) ( * 1 c Kp m L 1 1 ) ( ma ) ( ma ) ( Kd Kd L c Kd Kp m ) ( ) ( ) ( * 0 ) ( ma ) ( 1 Kd L 0 Kd

25 The nd Lyapunov Constran CL Predct faster and more accurately: A moton drven by a controller can keep balance forever f no further dsturbance. Demo to demonstrate advantage of Cl

26 Optmzaton Framework To show performance of the proposed optmzaton framework Demo to demonstrate advantage of Optmzaton Framework

27 Future work More controllers needed Start GUI not mplemented Select a moton controller C from moton database Desgn ntal & desred poses Smulate moton wth default C. End Montor nteracton from user. Yes No Generally fnshed Catch an nteracton? Yes Judge C workable? No Ultmate Goal System to effcently desgn requred fghtng sequence. Potentally apply our system nto fghtng acton desgn for game and move Solve controller parameters by optmzaton framework wth constrants Resume smulaton wth solved controller parameters

28 Publcaton Plan Publcaton Level TOG SgGraph Employng basc controllers to compose varous fghtng sklls under our optmzaton framework EuroGraphcs PacfcGraphcs Robust jumpng controller Rotatng controller System to effcently desgn fghtng sequence CAVW SCA Optmzaton Framework wth CL1 and CL Estng controllers Desgn new controllers Estng work + mprove hgh qualty demo Tme 1 st year nd Year 3 rd Year

29 Thank you very much!