Feedback control of humanoid robots: balancing and walking

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1 Feedbac control of humanoid robots: balancing and waling Dr.-Ing. Christian Ott German Aerosace Center DLR Institute for Robotics and Mechatronics DLR 2/5/212 1

2 Overview Part : Short overview of bied robots at DLR Part I: Modeling Part II: Balancing Part III: Waling Control Folie 2

traffic ~63 researchers 13 locations 29 institutes Institute of Robotics and

3 German Aerosace Center DLR National research laboratory Part of the Helmholtz association Research fields: o aerosace, o sace technologies, o energy and traffic ~63 researchers 13 locations 29 institutes Institute of Robotics and Mechatronics: Former director: Prof. Hirzinger Director: Prof. Albu-Schäffer Folie 3

4 Sace Robotics Institute of Robotics & Mechatronics ESS ROEX 1993 ROKVISS GEEX Maniulation LBR-I,199 LBR-II 1999/2 LBR-M, 23 orue sensors at the ower outut after the bearings orue sensors after the gears, but before the last bearings Modular design, load/weight ratio ~ 1:1 Commercial torue Folie 4 controlled arm KUKA

5 Joint torue sensing & control for maniulation Comliant Maniulation Environment et Rigid-Body Dynamics Motor Dynamics Comliance Control u orue Control m Robustness: Passivity Based Control Performance: Joint orue Feedbac noncollocated

6 Comliant Maniulation Environment et Rigid-Body Dynamics Motor Dynamics Comliance Control u orue Control m Robustness: Passivity Based Control Performance: Joint orue Feedbac noncollocated

29-213 Joint torue sensing & control for maniulation Bied Robot

Humanoids 21] Comliant actuation Antagonistic actuation for fingers

8 Joint torue sensing & control for maniulation Bied Robot Anthroomorhic Hand-Arm System [Grebenstein, Albu-Schäffer et al, Humanoids 21] Comliant actuation Antagonistic actuation for fingers Variable stiffness actuation in arm Robustness to shocs and imacts Folie 8

Small foot design: 19 9,5 cm Sensors: - joint torue sensors - force/torue sensors

9 Biedal Waling Robots at DLR Drive technology of the DLR arm Allow for osition controlled waling ZMP and joint torue control! Small foot design: 19 9,5 cm Sensors: - joint torue sensors - force/torue sensors in the feet - IMU in the trun DLR-Bied ORO, reliminary version 212 ORO 213 Orue controlled humanoid RObot Folie 9

10 First eeriments with DLR-Bied First eeriment at Automatica Fair in 6-21: ZMP review control [Kajita, 23] Current aroach: Waling control based on the Cature Point [Englsberger, Ott, Roa, et al. IROS 211] Folie 1

11 ORO Folie 11

12 Overview Part I: Modeling Multibody dynamics ZMP Simlified models for control Cature Point Centroidal Moment Pivot Part II: Balancing Part III: Waling Control Folie 12

13 Models of Legged Humanoid Robots Dynamical Models Mechanical Multi-Body-Models Concetual Models Floating Base Models Fied Base Models Waling Running redefined contact state Secialization Comleity

14 Free-Floating vs. Fied Base Models single suort serial in. chain double suort over-contrained underactuated Fied base models In each contact state the model is different: Single suort right, left Double suort Heel Off oe ouch Down Free-floating model Comonents: Lagrangian dynamics Constraints due to contact forces ransition euations imacts ransition between contact states

15 Free-Floating vs. Fied Base Models single suort serial in. chain double suort over-contrained underactuated Free-floating model Comonents: Lagrangian dynamics Constraints due to contact forces ransition euations imacts Fied base models In each contact state the model is different: Single suort right, left Double suort Heel Off oe ouch Down ransition between contact states Planning & control must ensure that the considered contact state is valid! ground reaction force must fulfill constraints Folie 15

16 Configuration Sace H b SE3 Q n n S 1 S 1 S 1 Configuration Sace: Q SE3

17 Configuration Sace b 6 H b SE3 Q n n S 1 S 1 S 1 Configuration Sace: Q SE3 Using local coordinates: n 6

18 Modeling, 6 F et se3 M C, g J Fet Folie 18

19 Modeling, F et F et F b 6 M C, g J Fet b 6 Folie 19

20 Folie 2 Modeling F et et F J g C M, F et et b b b b b b F J J F g C M M M M,,,, 6 b 6 F b

21 Folie 21 Modeling F et et F J g C M, F et et bt b sb b b b b b F J Ad W H g C M M M M,,,, 3 3 se SE H b sb b body twist Global reresentation!

22 Modeling b 6 r l F et F r F l Folie 22

23 Folie 23 Modeling F et F r F l l l bl r r br b b b b F J J F J J g C M M M M,,, l r 6 b

24 Folie 24 Biedal Robot Model F r F l l l bl r r br b b b b F J J F J J g C M M M M,,, l r 6 b Proerties for control: Underactuated Varying unilateral constraints single suort, double suort, edge contact Constraints on the state & control

25 Folie 25 l l bl r r br b b b b F J J F J J g C M M M M,,, f c Mg l r í i i F J I u Mg C c M M, ˆ ˆ ˆ, ˆ ˆ ˆ, c b Biedal Robot Model

26 Folie 26 l l bl r r br b b b b F J J F J J g C M M M M,,, f c Mg l r í i i F J I u Mg C c M M, ˆ ˆ ˆ, ˆ ˆ ˆ l r i f i Mg Mc,, c b Conservation of momentum: Biedal Robot Model

27 Folie 27 l l bl r r br b b b b F J J F J J g C M M M M,,, f c Mg l r í i i F J I u Mg C c M M, ˆ ˆ ˆ, ˆ ˆ ˆ l r i f i Mg Mc,, c b i Mg c L Conservation of angular momentum: Conservation of momentum: Biedal Robot Model

28 Folie 28 l l bl r r br b b b b F J J F J J g C M M M M,,, f c Mg l r í i i F J I u Mg C c M M, ˆ ˆ ˆ, ˆ ˆ ˆ l r i f i Mg Mc,, c b i Mg c L Conservation of angular momentum: Conservation of momentum: On a flat ground: Mg Mc Mg c L Biedal Robot Model f

29 Folie 29 l l bl r r br b b b b F J J F J J g C M M M M,,, f c Mg l r í i i F J I u Mg C c M M, ˆ ˆ ˆ, ˆ ˆ ˆ, c b On a flat ground: Mg Mc Mg c L Biedal Robot Model

30 Zero Moment Point

31 Zero Moment Point [Vuobratovic and Steaneno,1972] ZMP as a ground reference oint: Distributed ground reaction force under the suorting foot can be relaced by a single force acting at the ZMP. F 1 2 z y, y F ZMP = CoP Center of Pressure 1 2, y in conve hull of the suort olygon. Folie 31

32 Some facts about the ZMP Can ZMP leave the suort olygon? NO Can ZMP location be used as a stability criterion NO If ZMP reaches the border of the suort olygon foot rotation ossible. ZMP is defined on flat contact no uneven surface. ZMP gives no information about sliding. F 1 2 Folie 32

33 First usage of the ZMP Motion of the legs is redefined. Uer body controls the ZMP in the center of the suorting foot ensure roer foot contact during waling

34 How to obtain the ZMP? Measurement e.g. by Force/orue Sensor Dynamics Comutation

35 How to obtain the ZMP? Measurement e.g. by Force/orue Sensor Dynamics Comutation s s f s z f s s z z sy y z sz y z z s z sz y f f f f f f s

36 How to obtain the ZMP? Measurement e.g. by Force/orue Sensor Dynamics Comutation s s f s z z sy y z sz y z z s z sz y f f f f f f f f z f s s s

37 How to obtain the ZMP? Dynamics Comutation f f Mg c L f Mg P c y Mg P Mg c L z y z y y z y z P Mg L P Mgc P Mg L P Mgc

38 A simlified waling model based on the ZMP

39 Mass concentrated model f f

40 Mass concentrated model P Mc L c Mc z c f f

41 Mass concentrated model f f c z y z y y z y z P Mg L P Mgc P Mg L P Mgc z Mc c L Mc P z y z y y z z c g c c c c g c c c ZMP of a mass concentrated model

42 Mass concentrated model Cart-able Model [Kajita] c y c c y czc g c c c z y z g c z c z c z c c c c z g c

43 Mass concentrated model c g c c c z c Cart-able Model [Kajita] Linear Inverted Pendulum Model [Sugihara] z c c g c c c c

44 Cature Point Etraolated Center of Mass Divergent Comonent of Motion

45 Cature Point Definition of the Cature Point Pratt 26, Hof 28: Point to ste in order to bring the robot to stand. c, c Can be comuted eactly for simle models, e.g. linear inverted endulum model: c 2 g c z * ZMP Comutation of the Cature Point: const t cosh t sinh t 1 cosh t t *

46 Cature Point Dynamics Coordinate transformation:,, 2 System structure: Cascaded system cature oint COM oen loo unstable e. stable Dual use of the cature oint for robotics 1. ste lanning 2. control

47 Cature Point in Human Measurements Linear Inverted Pendulum Human y Data from [*] y [*] Hof, he etraolated center of mass concet suggests a simle control of balance in waling, Human Movement Science 27, , 28.

48 Centroidal Moment Pivot

49 Centroidal Moment Pivot Observation in human data: For normal level-ground waling, the human body s angular momentum and the angular ecursions about the COM remains small through the gait cycle. he centroidal moment ivot was introduced as a ground reference oint to address the effects of angular momentum about the COM in connection with ostural balance strategies.

50 Centroidal Moment Pivot Forces in the LIP model Effect of an additional hi torue Mg M g z z F M F M CMP g z CMP g z z F z Mz

51 Interretation he distance between CMP and ZMP corresonds to the angular momentum about the COM. While the ZMP cannot leave the suort olygon by definition, the CMP can leave it. he distance between CMP and the suort olygon has been roosed as an indicator which balance strategy should dominate via ZMP or via angular momentum.

52 Overview Part I: Modeling Part II: Balancing 1. Basics 2. ZMP based balancing concentrated mass model 3. orue based balancing multi body dynamics Part III: Waling Control Folie 52

53 Humanoid Balance Balance is a generic term describing the ability to control the body osture in order to revent falling. Vision Vestibular system IMU Vision Somatosensory system joint sensing force sensors Folie 53

54 Humanoid Balance Strategies for human ush recovery: Small ush: Anle strategy Medium ush: Hi strategy Large Push: Ste strategy Human Robot force control ZMP control angular momentum control Folie 54

55 mass concentrated model Strategies for gait stabilization: Effect of an additional hi torue 1. Controlling ZMP constraints! 2. Angular momentum control 3. Ste adatation Mg F M g z Mz Folie 55

56 Overview Part I: Modeling Part II: Balancing 1. Basics 2. ZMP based balancing concentrated mass model 3. orue based balancing multi-body model Part III: Waling Control Folie 56

57 Motivation for comliant control comletely stiff comliant control fully comliant Folie 57

58 ZMP based balancing z z Mg F M F Mg F et M et ref ref Feedbac Stabilization d Inverse Kinematics Forward Kinematics ZMP Comutation d d osition/velocity controlled robot Joint Position Control Robot Dynamics F R, F L Folie 58

59 ZMP based balancing z z Mg F M F Mg F et M et ref ref Feedbac Stabilization d Inverse Kinematics Forward Kinematics ZMP Comutation d d osition/velocity controlled robot Joint Position Control Robot Dynamics F R, F L Control law for stabilization: d ref K X d ref K P ref Stability condition [*]: K K X P Effective Stiffness: K X K 1 K P Mg z Stability condition [*]: [Choi, Kim, Oh, and You, Posture/Waling Control for Humanoid Robot Based on Kinematic Resolution of CoM Jacobian With Embedded Motion, RO, 27]. Folie 59

60 ZMP Based balancing Balancing + Vertical Motion Balancing + Vertical Motion + Comliant Orientation

61 Overview Part I: Modeling Part II: Balancing 1. Basics 2. ZMP based balancing concentrated mass model 3. orue based balancing multi-body model Part III: Waling Control Folie 61

62 Balancing & Posture Control Comliant COM control [Hyon & Cheng, 26] Mg F COM Mg K P c cd K D c c d F et F COM c R SO3 run orientation Control HIP et HIP V R, K R D R d IMU measurements Folie 62

63 Balancing & Posture Control Comliant COM control [Hyon & Cheng, 26] Mg F COM Mg K P c cd K D c c d F et F COM Desired wrench: W d FCOM, HIP R SO3 run orientation Control HIP et HIP V R, K R D R d IMU measurements Folie 63

64 Balancing & Posture Control Comliant COM control [Hyon & Cheng, 26] F COM Mg K P c cd K D c c d Mg F et Desired wrench: W d FCOM, HIP W d run orientation Control HIP V R, K R D R d IMU measurements Folie 64

65 Grasing and Balancing Force distribution: Similar roblems! Folie 65

66 Force Distribution in Grasing f i Net wrench acting on the object: W O F1 Gras Ma F F C se3 G 1F1 G F G1 G se3 Gi Ad PiO F C FC Well studied roblem in grasing: Find contact wrenches such that a desired net wrench on the object is achieved. friction cone Folie 66

67 Force distribution Relation between balancing wrench & contact forces G i Ri ˆ R i i W d f f 1 G G 1 G G F f C HIP F COM 3 Constraints: f i Unilateral contact: f i, z imlicit handling of ZMP constraints Friction cone constraints Folie 67

Force distribution Relation between balancing wrench & contact forces G i Ri ˆ R i i W d f f 1 G G 1 G G F f C HIP F COM 3 Constraints: f i Unilateral contact: f i, z

68 Force distribution Relation between balancing wrench & contact forces G i Ri ˆ R i i W d f f 1 G G 1 G G F f C HIP F COM 3 Constraints: f i Unilateral contact: f i, z imlicit handling of ZMP constraints Friction cone constraints Formulation as a constraint otimization roblem f C arg min 1 F COM G F f C 2 2 HIP G f C 2 3 f C Folie 68

69 Contact force control via joint torues Multibody robot model: COM as a base coordinate system structure with decouled COM dynamics. [Sace Robotics], [Wieber 25, Hyon et al. 26] M c Mˆ ˆ C ˆ ˆ, ˆ Mg u I ˆ í r, l Ji Fi M c Mg fi J ˆ i f i Passivity based comliance control well suited for balancing c f i 3 Folie 69

70 orue based balancing IMU Object Force Generation Force Distribution f c Force Maing orue Control Robot Dynamics for orientation control and COM comutation Folie 7

71 Uncertain Foot Contact [Ott, Roa, Humanoids 211, best aer award] Folie 71

72 Eeriments on a Perturbation Platform Leg erturbation setu Movable elastic latform Eerimental evaluation of the robustness with resect to disturbances freuency & amlitude at the foot Folie 72

73 Out of hase disturbance synchronous disturbance 2mm, u to 8 Hz

74 Comarisons 1 Imact eeriments 2 Whole body interaction 3 Singularities

75 Comarison 1/3 1 Imact eeriments Position Based Control orue Based Control

76 Comarison 1/3 1 Imact eeriments Position Based Control Observations: Balancing after imact is comarable orue based controller does not control relative foot location orue Based Control

77 Comarison 2/3 3 Whole body interaction Position Based Control orue Based Control

78 Comarison 2/3 3 Whole body interaction Position Based Control Observations: Force sensor based controller deends on a reference frame orue based controller does not need information about the oint of contact orue Based Control

79 4 Singular Configurations Comarison 3/3 Position Based Control orue Based Control

80 4 Singular Configurations Comarison 3/3 Position Based Control Observations: Position based controller uses Inverse Kinematics, which reuires singularity handling orue based controller uses transosed Jacobian maing, and thus is not affected by singularities orue Based Control

81 Balancing: Summary On flat floor both aroaches allow for a comliant behavior orue based controller shows indeendence on recise ground contact force maing based on IMU information Admittance controller deends on a reference frame

82 Overview Part I: Modeling Part II: Balancing Part III: Waling Control 1. Waling attern generation 2. Feedbac control Folie 82

83 Robot control based on concetual models Footste Generation Pattern Generation c ZMP-COM Stabilizer d Pos. Controlled Robot F realtime e.g. LQR Preview Control [Kajita, 23] Model Predictive Control [Wieber, 26]

84 Mass concentrated model Linear Inverted Pendulum Model [Sugihara] Cart-able Model [Kajita] c c g z z g

85 Mass concentrated model c g z Cart-able Model [Kajita] u y u g z y 1 / 1 2 / 6 / / g c y u z Continuous time control model Discrete time model

86 LQR Preview Control How to use future information about the reference?

88 LQR Preview Control 1 C y Bu A u R u Q Q e e J e 1 1 u u u y y e ref ime-discrete system: Cost function: Uses differential control inut integral action. Uses the outut error comared to reference signal. y ref Reference outut: Assume nown for N future time stes Assume A,B is stabilizable & C,A is detectable, and [**] [**] Ensures that the system has no transmission zero at z=1. n y R Q e, ositive definite. n I A B C ran Assumtions:

89 LQR Preview Control 1 C y Bu A ime-discrete system: y I u B CB e A CA I e ref Modified system reresentation: u u [**] Ensures that this system is stabilizable.

90 LQR Preview Control 1 C y Bu A ime-discrete system: y I u B CB e A CA I e ref Modified system reresentation: u u How to handle future reference inut? System augmentation for net N reference inut values, 1, N y y ref ref d d A d d Dynamics of the new state: [**] Ensures that this system is stabilizable.

91 LQR Preview Control u B CB e A A I CA I e z d d z d Modified system reresentation: u R u Q Q e e J e Cost function: u R u z Q Q z J e Standard LQR Design for augmented system!

92 Preview Control e K K K Kz u d d e N i ref d i ref e i y i K K i y i y K u 1 Control law:

93 Eamle Alication: Waling Pattern Generation Simlified Model: Cart able Model u ZMP Zero Moment Point loosely seaing: Point on the sole where the reduced contact force is acting. Position of the CoM / 1 2 / 6 / / g z y u y Kajita 23

94 Eamle Alication: Waling Pattern Generation Footste lanning d d Waling Pattern Generator CoM IK Joint Position Control Preview Control: = 5 ms N = 4 Q_ = zeros3,3; Q_e = 1.; R = 1e-6;

95 Eamle Alication: Waling Pattern Generation Footste lanning d d Waling Pattern Generator CoM IK Joint Position Control Preview Control: = 5 ms N = 4 Q_ = zeros3,3; Q_e = 1.; R = 1e-6;

96 Proerties of Preview Control Efficient imlementation, controller design can be comuted offline Allows to incororate redictive information ZMP contstraints are not considered elicitely rajectory based aroach Etensions Model redictive control handle zm constraints elicitely, otimization over a finite control horizon rajectory generation feedbac control Dynamic filter

97 Feedbac Stabilization swing foot trajectory osition/velocity controlled robot Footste lanning d Waling Pattern Generator ref ref Feedbac Stabilization d Inverse Kinematics d d Joint Position Control Robot Dynamics Forward Kinematics ZMP Comutation F R, F L Control law for stabilization: d ref K X d ref K P ref Stability condition [*]: K X K P Stability condition [*]: [Choi, Kim, Oh, and You, Posture/Waling Control for Humanoid Robot Based on Kinematic Resolution of CoM Jacobian With Embedded Motion, RO, 27].

98 Dynamic filter Correction of the error due to model simlification Reuires comutation of the multi-body dynamics Footste lanning d Preview Control ref Inverse Kinematics d Robot Dynamics Preview Control ref Inverse Kinematics

99 DLR-Bied ZMP basierte Gangregelung Präsentiert auf der Industriemesse Automatica, Juni 21

100 Overview Part I: Modeling Part II: Balancing Part III: Waling Control 1. Waling attern generation 2. Feedbac control

101 Waling Control State of the art waling control for fully actuated robots Pattern Generator for desired CoM and ZMP motion ZMP based Stabilizer realtime Footste Generation Pattern Generation c ZMP-COM Stabilizer d Inverse Kinematics d Position Control e.g. Preview Control [Kajita, 23] Model Predictive Control [Wieber]

102 Waling Control used at DLR [Englsberger, cature oint control] Waling Stabilization Core concet: Cature oint control Generalization 3D Stairs, etc c, 2, Predictive Control MPC Reactive ste adatation Pratt 26, Hof 28, cature oint COM oen loo unstable e. stable Folie 12

103 Waling Control used at DLR [Englsberger, cature oint control] Waling Stabilization Core concet: Cature oint control Generalization 3D Stairs, etc c, 2, Predictive Control MPC Reactive ste adatation Pratt 26, Hof 28, cature oint COM CP control e. stable Folie 13

104 Cature Point Dynami Cature Point COM velocity always oints towards CP ZMP ushes away the CP on a line COM follows CP ZMP COM Folie 14

105 Cature Point Dynami Cature Point ZMP COM Folie 15

106 Cature Point Control rajectory Generator d CP control ZMP rojection ZMP Control Robot Dynamics CP, COM inematics [Englsberger, Ott, et. al., IROS 211] Folie 16

107 Cature Point Control rajectory Generator d CP control ZMP rojection MPC [SYROCO 212] ZMP Control Robot Dynamics CP, COM inematics [Englsberger, Ott, et. al., IROS 211] Folie 17

108 Position based ZMP Control rajectory Generator d CP control ZMP rojection MPC ZMP Control Robot Dynamics CP, COM inematics Desired ZMP imlies a desired force acting on the COM: d 2 F 2 M d d Position based ZMP Control Position based force control [Roy&Whitcomb,22]: d f 2 M d d f F F d Folie 18

109 Cature Point Control rajectory Generator d CP control ZMP rojection MPC [SYROCO 212] ZMP Control Robot Dynamics CP, COM inematics [Englsberger, Ott, et. al., IROS 211] Folie 19

110 Alications 1 Vision based waling stereo vision Hirschmüller visual SLAM Chilian, Steidel online footste lanning, collaboration with N. Perrin II

111

112 Alications 2 Otimized swingfoot trajectories: collaboration with H. Kaminaga Univ. oyo stride length: 7 cm seed:.5 m/s inematically otimized swingfoot trajectory stride length: 7 cm seed:.5 m/s inematically otimized torso motion no angular momentum conversation! sliery

113 Summary Part I: Part II: Part III: Modeling Balancing Waling Full Body Models Simlified Models orue based Balancing ZMP based balancing Pattern generation Feedbac control Folie 113

114 han you very much for your attention! Dr. Maimo Roa Johannes Englsberger Aleander Werner Gianluca Garofalo Bernd Henze Dr. Christian Ott Folie 114

Control Approaches for Walking and Running

DLR.de Chart 1 > Humanoids 2015 > Christian Ott > 02.11.2015 Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de Chart 2 > Humanoids 2015