On Humanoid Control. Hiro Hirukawa Humanoid Robotics Group Intelligent Systems Institute AIST, Japan

Transcription

1 1/88 On Humanoid Control Hiro Hirukawa Humanoid Robotics Group Intelligent Systems Institute AIST, Japan

2 2/88 Humanoids can move the environment for humans Implies that Walking on a flat floor and rough terrain Going up and down stairs and ladders Lying down, crawling and getting up Falling down safely and getting up Opening and closing doors Humanoids move on two, three or four feet.

3 3/88 Humanoid as a Controlled Plant A humanoid robot is a multi- link structure that is not fixed to the environment and moves in the environment and/or moves the environment by the contact force between the robot and the environment in the gravity field.

4 4/88 Humanoid Control Problem When the initial and final configurations of a humanoid robot is given, find motions of the robot that can transfer it from the initial configuration to the final configuration through a sequence of the contact states.

5 5/88 Control Algorithms Inverted Pendulum Scheme 1. Plan motions of the robot 2. Change the position of the next footprint to keep the planned configuration of the robot ZMP (Zero Moment Point) based Scheme 1. Plan a sequence of footprints. 2. Change the configuration of the robot to keep the planned sequence of the footprints

6 6/88 Motions vs. Contact Force M ( g p&& ) = f G p M ( g p ) L = τ G G C C p C G C : L : f : τ : Position of the center of the gravity Angular momentum about the COG Contact force Contact torque

7 7/88 Inverted Pendulum Scheme [Gubina, Hemami and McGee 1974]

8 8/88 Footprints may have a constraint

9 9/88 ZMP based Scheme [Vukobratovic and Stepanenko 1972] And more.

10 10/88 What is ZMP (Zero Moment Point)? Vukobratovic and Stepanenco, 1972 Center of Pressure ZMP NEVER leaves the support polygon! ZMP can be measured by force sensors in feet.

11 11/88 How ZMP is used? When the ZMP is inside the support polygon, the contact between the feet and the floor should be kept. When the contact is kept, the posture of the robot should be kept without falling down.

12 12/88 From the ZMP to the COG zmp [m] Target ZMP pattern zmp ref time [s] Trajectory of the center of mass y [m] CoM time [s]

13 13/88 Motions vs. Contact Force M ( g p&& ) = f G p M ( g p ) L = τ G G C C p C G C : L : f : τ : Position of the center of the gravity Angular momentum about the COG Contact force Contact torque

14 14/88 Cart-Table Model M z c O ZMP = 0 x0 x A running cart on a mass-less table The table has a small support area

15 15/88 The ZMP of the Cart-Table Model M z h x&& Balance of moment τ = Mg( x x) Mxz && ZMP = 0 0 h τ ZMP = 0 O x 0 x ZMP equation z h x0 = x && x g

16 16/88 Input and Output y [m] 0.1 CoM time [s] x Cart trajectory M z h x0 = x && x g zmp [m] 0.1 zmp ref time [s] x 0 ZMP Walking pattern generation Find the cart trajectory to realize the given ZMP pattern

17 17/88 Servo tracking control of the ZMP ref x0 x 0 + Target ZMP Controller u M x 0 ZMP x x 0 d x & = x & 0 u dt + && x && x 1 x zh x0 = 1 0 x & g && x Proper dynamics of Cart-Table model

18 From ZMP reference to Cart motion ZMP reference x ref x 0 + x Controller ZMP Ordinal servo control Walking pattern x [m] x [m] reference x time [s] time [s] zmp ref x The cart must move before ZMP changes! Servo controller must use FUTURE information Hiro Hirukawa The Onassis Foundation Lecture Series /88

19 19/88 The Preview Control u On a winding road, we steer a car by watching ahead, by previewing the future reference. Control law Concept and naming [Sheridan 1966] LQ optimal controller [Tomizuka and Rosenthal 1979] [Katayama et.al 1985] ref k 0( k + 1) ref k = K I ( x0k x0k ) Kxxk [ f1, f2, L fn ] M i= 0 ref x 0( k + N ) Accumulate Servo error State feedback Preview gain x Target ZMP of N-step future

20 Preview gain preview gain T 1 T T ( i 1) T fi = ( R+ B PB) B ( A BK) C Q T 1 T K ( R+ B PB) B PA LQ optimal feedback gain f i future time [s] The preview gain is approximately zero after 1.6s future. Controller does not need the future ZMP farther than 1.6s. Hiro Hirukawa The Onassis Foundation Lecture Series /88

21 ZMP Tracking Example zmpx [m] x zmp zmp_ref zmpy [m] y zmp zmp_ref time [s] Hiro Hirukawa The Onassis Foundation Lecture Series /88

22 22/88 Walking Pattern Generator HRP-2L [Kajita et al.] HRP-2P

23 23/88 Experiment of HRP-2

24 24/88 Configuration of the Feedback Controller Balancer Module Gyro Accelerometer Kalman filter Body inclination Force/torque sensor encoder ZMP calculator ZMP Stabilizer Joint servo References of Joint angles, body inclination and ZMP

25 25/88 Feedback Controller is essential Without stabilizer With stabilizer

26 26/88 Feedback Control of the Table Orientation x M Equation of motion: && && & & 2 2 ( + ) θ+ ( sinθ+ cos θ ) + 2 θ= 0 µ f Linearize at θ 0 = 0 zc && && 2 2 ( + ) θ= θ Cart on a table Table inclination Cart acceleration

27 27/88 Feedback Control of the Cart Position [Nagasaka, Inaba and Inoue, 1999] z c O p x ZMP = 0 M Used in the walking controller of H7. Good for robots with hard feet. ZMP equation with sensor delay T d dt z h 1 x0 = ( x && x) 1 + st g System representation x0 1/ T 1/ T 0 x0 zc /( gt) x = x + 0 && x x& x 1 Stabilization by state feedback && x= k x k x k x& Cart position modification ZMP error

28 Experiment on a Slope (1/2) Hiro Hirukawa The Onassis Foundation Lecture Series /88

29 29/88 HRP-2 2 walks on a Rough Terrain Gap < 20 mm Slope < 5%

30 30/88 Japanese Traditional Dance [Nakaoka et al. 2005]

31 31/88 The First Running Humanoid Sony Qrio [Dec.,2003] Qrio runs at 0.84 km/h.

32 32/88 Running Biped [AIST Apr.,2004] Speed 0.58km/hour Slow motions

33 33/88 Walking on a floor with low friction : : between a tire of a car and a wet snow surface

34 34/88 Reduction of the Slip by a Tuning of Walking Pattern Rotation about Yaw-axis may occur at. due to the change of the acceleration when the supporting leg is exchanged. The pattern generator is tuned to reduce the peak of the jerk. 0.8 showzmp0.m (sliptest3_mu03\sim-astate.log) /ZMP trajectory showzmp0.m (sliptest3b_mu03\sim-astate.log) /ZMP trajectory Walk direction Walk direction y [m] 0 y [m] x [m] =0.3 Conventional pattern x [m] =0.3 Improved pattern

35 35/88 Walk on a Floor with a Low Friction

36 36/88 Humanoids can move the environment for humans Implies that Walking on a flat floor and rough terrain Going up and down stairs and ladders Lying down, crawling and getting up Falling down safely and getting up Opening and closing doors Humanoids move on two, three or four feet.

37 37/88 Contact States Graph

38 38/88 Balance Control for the Transition The position of the torso link is under a compliance control. Landing ZMP[m] toe heel

39 39/88 Dynamic Simulation

40 40/88 Lying down and Getting up

41 41/88 Humanoids can move the environment for humans Implies that Walking on a flat floor and rough terrain Going up and down stairs and ladders Lying down, crawling and getting up Falling down safely and getting up Opening and closing doors Humanoids move on two, three or four feet.

42 42/88 Preliminary Experiment for Falling With the knee extended With the knee bended

43 43/88 Falling Motion of a Leg Robot

44 44/88 Impact Test

45 45/88 Falling Motion of Humanoid Robot

46 46/88 Humanoids can move the environment for humans Implies that Walking on a flat floor and rough terrain Going up and down stairs and ladders Lying down, crawling and getting up Falling down safely and getting up Opening and closing doors Arms and legs coordination Humanoids move on two, three or four feet.

47 Several Configurations of Arm/Leg Coordination Walking and and Touching Leaning on on Balancing Pulling Hiro Hirukawa The Onassis Foundation Lecture Series 2006 Pushing 47/88

48 A Generalized ZMP [Harada et al. 2004] 2D Convex Hull Hiro Hirukawa The Onassis Foundation Lecture Series D Convex Hull 48/88

49 49/88 A Generalized ZMP [Harada et al. 2004]

50 50/88 A Generalized ZMP [Harada et al. 2004] Small Acceleration ZMP

51 51/88 A Generalized ZMP [Harada et al. 2004] Large Acceleration Moment around the edge ZMP

52 52/88 Projection of the ZMP Y ~ p G ( =~ p G ) X Z

53 53/88 Numerical Example

54 54/88 Area of the Generalized ZMP Front Front

55 55/88 Push a heavy object 25.9 kg [Harada et al. 2004]

56 56/88 Pushing a button with the support of a hand [Harada et al. 2004]

57 57/88 An Open Question Can we plan motions of humanoid robots based on the unified criterion? What the ZMP criterion can judge? The ZMP can judge if the contact should be kept without solving the equations of motions when the robot moves on a flat plane under the sufficient friction assumption.

58 58/88 Our Goal are to create a new criterion that can judge the contact stability of humanoids which may touch an arbitrary terrain with two, three or four feet, and to prove that the criterion is equivalent to ZMP in a specific case and more universal, and to claim to say Adios ZMP.

59 59/88 Related Works Legged Robots ZMP [Vukobratovic[ 1972] Locomotion with hand contact [Yoneda[ 1996] FRI [Goswani[ 1999] FSW [Saida[ 2003] Generalized ZMP [Harada 2004] Mechanical Assembly Strong and Weak Stability [Trinkle[ 1997]

60 60/88 Formulation Gravity and Inertia Wrench fg = M ( g p&& G) τ = p M ( g p ) L G G G p G p G : Center of the mass : Angular momentum around COG L Contact Wrench K L l l C = ε k( k + µ k k) k= 1 l= 1 K L l l C = ε k k k + µ k k k= 1 l= 1 f n t τ p ( n t ) Polyhedral Convex Cone

61 61/88 Strong Stability Criterion The contact state must be stable if (-fg,- G)( is an internal element of the contact wrench cone under the sufficient friction assumption. (proof) The work done by (fg, G) is negative for any motion; ( δ x, Ω ) 0,( f τ ) int( CWC);( δx, Ω ) ( f τ ) < 0, G G G, G G G G, G where the CWC is given by K L l l l C = εk k + εk k k= 1 l= 1 f ( n t ) K L l l l C = εk k k + εk k k k= 1 l= 1 τ ( p n p t )

62 Example 1. Walking on a horizontal plane with sufficient friction K 1 2 Mx G = ( εk εk) k= 1 K 3 4 My G = ( εk εk) k= 1 K 0 M( zg + g) = εk k= 1 K 0 G + G G G + L x = εk k k= 1 K 0 G G G G L y εk k k= 1 K Mx GyG MyGx G + L z = εk εk xk εk εk yk k= 1 M ( z g) y My z y M ( z + g) x + Mx z + = x Hiro Hirukawa The Onassis Foundation Lecture Series 2006 Horizontal force should balance the friction from the assumption Strong stability holds if the moment along the horizontal axes is inside the CWC. {( ) ( ) )} 62/88

63 63/88 Strong Stability Determination by ZMP M( z ) K G + g xg Mx GzG L y = λ M( z + g) G K M( zg + g) yg My GzG + L x = λ M( z + g) G k= 1 k= 1 k k x y k k K k= 1 λ k = 1, λ 0 k

64 Equivalence between the ZMP and the CWC ZMP M( z ) K G + g xg Mx GzG L y = λkx M( zg + g) K M( zg + g) yg My GzG + L k= 1 x = λkyk M( z + g) K k= 1 G λ k = 1, λ 0 k k= 1 k CWC Hiro Hirukawa The Onassis Foundation Lecture Series 2006 K 0 G + G G G + L x = εk k k= 1 K 0 G G G G L y εk k k= 1 K 0 M( zg + g) = εk k= 1 M ( z g) y My z y M ( z + g) x + Mx z + = x Dividing the equations by 64/88

65 Equivalence between the ZMP and the CWC ZMP M( z ) K G + g xg Mx GzG L y = λkx M( zg + g) K M( zg + g) yg My GzG + L k= 1 x = λkyk M( z + g) G k= 1 k K k= 1 λ k = 1, λ 0 k CWC Hiro Hirukawa The Onassis Foundation Lecture Series 2006 M( z + g) y My z + L ε = M( z + g) ε K 0 G G G G x k G k= 1 M( z + g) x + Mx z + L ε = M( z + g) ε K 0 G G G G y k K k= 1 G ε ε ε = 1, 0 ε 0 0 k k k= 1 y k x k 65/88

66 66/88 The CWC for a 2D-Robot on a Line fz z x fx

67 67/88 A Desired Trajectory in the CWC fz fz fx The CWC is the direct product of a 2D polyhedral cone and 1D linear subspace, which is identical for the single and double support phases. fx

68 68/88 Example 2. Robot on a Stair (1/2) y λ2 y λ z 1 F 2 x λ1 x λ1 z F1 M( z + g) y M y z + L G G G G K 0 y y εkyk λ1 zf1 λ2 k= 1 = z x F 2 M( z + g) x + Mx z + L G G G G y K 0 x x = εkxk + λ1 z F 1+ λ2z F 2 k= 1

69 Example 2. Robot on a Stair (2/2) y λ2 x λ1 M( z + g) y My z + L K k= 1 G G G G G x = ε y λ z λ z My 0 y y k k 1 F1 2 F2 K y y 0 λ 1 λ 2 = εkyk My G z y y F1 z y y F2 k= 1 λ1 λ + 2 λ1 λ where = λ + λ y y 1 2 y λ1 x λ1 z F 2 z F1 Hiro Hirukawa The Onassis Foundation Lecture Series 2006 K 0 G + G G G zf + L x = εk k k= 1 y y λ 1 λ 2 zf = z y y F1 + z y y F2 λ1 + λ 2 λ1 + λ 2 M ( z g) y My ( z ) y 69/88

70 70/88 Pattern Generation of the COG d dt ξ u ξ yg yg 0 y& = y& + 0 u y G y G 1 && && G G y tx G F G y tx = ( Mg 0 M( z z y )) y& && y = && y G = τ ref y L& ref y G G

71 71/88 The CWC for a 2D-Robot on a Stair fz z x fx

72 A Desired Trajectory in the CWC fz fz fx The CWC is the direct product of a 2D polyhedral cone and 1D linear subspace, which is not identical for the single support phases of the lower and the higher feet, and is the product of the 2D cone and 2D linear subspace for a double support phase. Hiro Hirukawa The Onassis Foundation Lecture Series 2006 fx 72/88

73 73/88 Vertical Trajectory of the ZMP Not admissible in the single support phase Pseudo Plane on which the ZMP trajectory is defined [Honda] Equivalent trajectory of the ZMP based on the proposed criterion

74 74/88 Horizontal Contact Force while Climbing Stairs single double single single double single Black curve is generated from a continuous trajectory in the CWC Red curve is generated from a discontinuous one in the CWC

75 75/88 ZMP CWC ZMP CWC Flat plane Foot contact Sufficient friction Arbitrary terrain Hand/Foot contact Sufficient friction Strong Stability N/A Strong Stability Strong Stability

76 76/88 Summary of the CWC The proposed criterion is equivalent to ZMP in the specific case and can judge the strong stability in generic cases. Therefore we claim to say Adios ZMP,, and the voice can be louder when we can plan motions in a variety of cases based on the proposed criterion.

77 77/88 Open Problems in the Control Robust walking Biped walking is still not robust enough for a large disturbance. Walking on a natural rough terrain Walking must be more generalized with the recognition of the working environment. Falling motion control The human-size humanoid just crashes when it falls down without a proper control.

78 78/88 Humanoids in Real Environment

79 79/88 Research Platforms HRP-2 (Kawada) 154cm, 0.5M Euro Available at LAAS, France HOAP (Fujitsu) 60cm, 50K Euro HRP-2m Choromet (General Robotix) 35cm, 5K Euro

80 80/88 Free Research Platform OpenHRP: Open Architecture Humanoid Robotics Platform

81 81/88 Implementation Features of OpenHRP Distributed Object System based on CORBA Concurrent development using an arbitrary operating system and language OpenHRP is written in Java, C++ and runs on Linux and Windows

82 82/88 CORBA Objects of OpenHRP

83 83/88 ISE : Integrated I Simulation Environment Model VRML file file file ISE Project file

84 84/88 Our Current Challenge A Famous Project of Takeo Kanade EyeVision at the Superball Let s s watch NBA in the court. Our Challenge Let s s go to the cafeteria with a humanoid. Robust biped walking Going up and down stairs Opening and closing doors 3D SLAM

85 85/88 Powered Suits HAL [U of Tsukuba] Bleex [UC Berkeley]

86 86/88 Autonomous Walking-Aid Range Sensor Stairs Obstacles Rough Terrain

87 87/88 A Measure of the Ability of a Robot Artificial Intelligence This robot has the intelligence that is compatible to three years old child. Mobility of a Humanoid This robot has the mobility that is compatible to eighty years old person.

88 88/88 May, my dog on a summer vacation