walking and stair climbing stabilization for position-controlled ...hrp-4humanoidrobotinshort....

Walking and stair climbing stabilization forposition-controlled biped robots.

Stéphane CaronMarch 19, 2019

Presentation given at Wandercraft, Paris

context.

COMANOID project - https://comanoid.cnrs.fr

1

https://comanoid.cnrs.fr

final demonstrator.

2

stair climbing part.

https://www.youtube.com/watch?v=vFCFKAunsYM

3


hrp-4 humanoid robot in short.

Stiff position control on all joints Mechanical flexibility at the ankles

1

1. Kenji Kaneko, Fumio Kanehiro, Mitsuharu Morisawa, Kazuhiko Akachi, Gou Miyamori, AtsushiHayashi et Noriyuki Kanehira. « Humanoid robot HRP-4 - Humanoid Robotics Platform with Light-weight and Slim Body ». In : IEEE/RSJ International Conf. on Intelligent Robots and Systems. 2011.

4

system overview.

WalkingPattern

Generation

Whole-bodyAdmittanceControl

Whole-bodyKinematicControl

DCMControl

DCMObserver

5

walking pattern generation.

FootstepLocations Walking

PatternGeneration



DCMControl

DCMObserver

DesiredKinematicTargets

6

linear inverted pendulum mode.

• Equation of motion :

Mq+ N = STτ + JTf

• Floating base dynamics :

c = 1m∑

i fiLc =

∑i(pi − c)× fi

• Angular momentum Lc = 0 :

c = ω2(c− z)

with ω2 = g/h and z the ZMP

2

2. Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kazuhito Yokoi et Hirohisa Hirukawa. « The 3DLinear Inverted Pendulum Mode : A simple modeling for a biped walking pattern generation ». In :IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001.

7

divergent component of motion.

• LIPM equation of motion :

c = ω2(c− z)

• Divergent Component of Motion :

ξ = c+ cω

• Unstable dynamics :

ξ = ω(ξ − z)

3

3. Johannes Englsberger, Christian Ott, Maximo Roa, Alin Albu-Schäffer, Gerhard Hirzinger etal. « Bipedal walking control based on capture point dynamics ». In : IEEE/RSJ International Confe-rence on Intelligent Robots and Systems. 2011.

8


Generate a CoM-ZMP trajectory that is :

Consistent

∀t > 0, c(t) = ω2(c(t)− z(t))

Feasible

• ZMP belongs to support area• Contact force within friction cone

ViableNot falling. For this system, same asbounded : ∃M > 0, ∀t > 0, ∥c(t)∥ ≤ M

Figure adapted from [Gri+17].

9


So far we have tested three methods :

• Linear Model Predictive Control [Wie06]• Foot-guided Agile Control through ZMP Manipulation [SY17]• Capturability of Variable-Height Inverted Pendulum [Car+18]

10

linear model predictive control.

Formulate preview control [Kaj+03] as a Quadratic Program (QP) :

Cost function

• Track desired ZMP reference• Track desired CoM velocity• Minimize CoM jerk

Constraints

• Consistency : state equation• Feasibility : ZMP in support area• Viability : terminal DCM

Allows a number of extensions, including :

• Variable CoM height : [Bra+15]• Variable step timings : [BW17]

4

4. Pierre-Brice Wieber. « Trajectory free linear model predictive control for stable walking in thepresence of strong perturbations ». In : IEEE-RAS International Conference on Humanoid Robots.2006.

11

foot-guided agile control through zmp manipulation.

Predictive control with ZMP as input

minimizez(t)

∫ T

0

(z(t)− zd)2dt ⇒ Feasibility (best effort)

subject to c = ω2(c− z) ⇒ Consistency

c(T) + c(T)ω

= ξd ⇒ Viability

• Finite horizon, continuous time dynamics• Analytical solution :

z∗(0) = zd + 2(ξ(0)− zd)− (ξd − zd)e−ωT

1− e−2ωT

• Call many times to adapt step timings

5

5. Tomomichi Sugihara et Takanobu Yamamoto. « Foot-guided Agile Control of a Biped Robotthrough ZMP Manipulation ». In : IEEE/RSJ International Conference on Intelligent Robots and Sys-tems. 2017.

12

variable-height inverted pendulum.

• New input λ > 0 for height variations :

c = λ(c− z) + g

• Viability⇒ boundedness condition :

ξ(0) =

∫ ∞

0

(λ(t)r(t)− g)e−Ω(t)dt

• Solve : tailored optimization (30-50 µs)• Call many times to adapt step timings

6

6. Stéphane Caron, Adrien Escande, Leonardo Lanari et Bastien Mallein. « Capturability-basedAnalysis, Optimization and Control of 3D Bipedal Walking ». 2018. url : https://hal.archives-ouvertes.fr/hal-01689331/document.

13

https://hal.archives-ouvertes.fr/hal-01689331/document


visualization.

Visualization of stair climbing pattern in mc_rtc

14

walking stabilization.


PatternGeneration



DCMControl

DCMObserver


15

role of stabilization.

Actuated joints converge but unactuated floating base diverges :

In walking pattern By robot without stabilization

Figure adapted from [Tak+09].

16

floating base facts.

Let's review the facts :• Floating base translation is unactuated• Its dynamics are reduced to :

c = ω2(c− z)

• Only way to control it is via indirectforce control of the ZMP z

17

indirect force control.

... but our robot is position-controlled ?

Split control into two components :

Admittance controlAllow position changes to improve forcetracking

Floating-base controlAssuming force control, select reactionforce to control the floating base

18

visualization.

Standing stabilization under external forces

19

admittance control.


PatternGeneration


CommandedJoint AnglesWhole-body

KinematicControl

DCMControl

DCMObserver


DistributedFoot Wrenches

CommandedKinematicTargets

MeasuredFoot Wrenches

20

strategies.

Different strategies for differentcomponents of the net contact wrench :• CoP at each contact [Kaj+01b]• Pressure distribution [Kaj+10]• CoM admittance control [Nag99]

This stabilizer implements :• Ankle strategy : yes• Hip strategy : translation, no rotation• Stepping strategy : no

21

center-of-pressure control.

• Rotate end-effector to move its CoP• Assumes compliance at contact :

τ = Ke(θ − θe)

• Apply damping control :

θ = Acop(τd − τ)

• Closed-loop behavior has τ → τd Figure adapted from [Kaj+01b]

7

7. Shuuji Kajita, Kazuhito Yokoi, Muneharu Saigo et Kazuo Tanie. « Balancing a Humanoid RobotUsing Backdrive Concerned Torque Control and Direct Angular Momentum Feedback ». In : IEEEInternational Conference on Robotics and Automation. 2001.

22

pressure distribution control.

• Net vertical force compensatesgravity⇒ only need to control :

∆fz = fRz − fLz

• Push down with foot that needs morepressure, lift the other one

• Apply damping control :

zctrl = Az(∆fzd −∆fz)

ctrlz*d

Rzp*dLzp

RzfLzf

Figure adapted from [Kaj+10]

8

8. Shuuji Kajita, Mitsuharu Morisawa, Kanako Miura, Shin'ichiro Nakaoka, Kensuke Harada, KenjiKaneko, Fumio Kanehiro et Kazuhito Yokoi. « Biped walking stabilization based on linear invertedpendulum tracking ». In : IEEE/RSJ International Conference on Intelligent Robots and Systems. 2010.

23

com admittance control.

• Recall that c = ω2(c− z)• Accelerate CoM against ZMP error :

c = Ac(z− zd)

• Closed-loop behavior : analysis isonly possible with delay ordisturbance observer 9

measured desired

10

9. Discussions with Pr T. Sugihara.10. Ken'ichiro Nagasaka. « Whole-body Motion Generation for a Humanoid Robot by Dynamics

Filters ». In : PhD thesis (1999). The University of Tokyo, in Japanese.

24

choice of strategies.

Which ones to choose ?

End-effector strategies

• CoP at each contact [Kaj+01b]• Pressure distribution [Kaj+10]

... are sufficient to control the net wrench,yet :

CoM admittance control [Nag99]

• uses other joints, e.g. hips• helps recover from ZMP saturation 11

11. The effect is similar to Model ZMP Control [Tak+09].

25

com admittance in stair climbing.

Sagi

ttal

Coo

rdin

ate

(m)

Time (s)

Measured ZMP

Measured DCM

Desired DCM

Desized ZMP

Maximum ZMP

Minimum ZMP

-0.1

0.0

0.1

0.2

0.3

-0.1

0.0

0.1

0.2

0.3

Figure 1 : Top : no CoM admittance control. Bottom : with Ac = 20 [Hz2].

26

dcm control.


PatternGeneration


CommandedJoint Angles

Measured Joint Angles


DCMControl

DCMObserver

EstimatedDCM

Measured IMU Orientation

Desired DCM

Desired CoM & Contacts





27

net wrench.

• Assume control of z in c = ω2(c− z)• Controlling only the DCM ξ = ω(ξ − z) :requires less control input [Tak+09]yields best CoM-ZMP regulator [Sug09]

• Apply feedback control to it :

ξ = ξd + kp(ξd − ξ)

z = zd −[1 +

kpω

](ξd − ξ)

This gives us the net wrench.

12

12. Tomomichi Sugihara. « Standing stabilizability and stepping maneuver in planar bipedalismbased on the best COM-ZMP regulator ». In : IEEE International Conference on Robotics and Auto-mation. 2009.

28

damping and integral terms.

• Add damping term, add integral term to eliminate steady-state error :

ξ = ξd + kp(ξd − ξ) + ki∫

(ξd − ξ) + kd(ξd − ξ)

z = zd − (1 +kpω)(ξd − ξ)− ki

ω

∫(ξd − ξ) +

kzω(zd − z)

• Select gains kp, ki, kz (1) by hand or (2) by pole placement• In practice : how to manage the link with admittance control gains ?

13

13. Mitsuharu Morisawa, Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kanako Miura et KazuhiroYokoi. « Balance control based on capture point error compensation for biped walking on uneventerrain ». In : IEEE-RAS International Conference on Humanoid Robots. 2012.

29

distribute net wrench to contacts.

Wrench distribution by QP :

Cost function

• Realize net wrench• Minimize ankle torques• Desired pressure distribution

Constraints

• Frictional wrench cones• Minimum pressure on each contact

30

complete system.


PatternGeneration


CommandedJoint Angles

Measured Joint Angles


DCMControl

DCMObserver

EstimatedDCM

Measured IMU Orientation

Desired DCM

Desired CoM & Contacts





31

experimental results.


32


coda : an ode to two tools.

mc_rtc control framework by p. gergondet.

Controller with mc_rtc GUI alongside a Choreonoid dynamic simulation

33

choreonoid simulator by s. nakaoka.

Failure case on real robot Reproduction in Choreonoid

http://choreonoid.org/en/

34

http://choreonoid.org/en/

thanks !.

Thank you for your attention !

35

references i.

[Bra+15] Camille Brasseur, Alexander Sherikov, Cyrille Collette, Dimitar Dimitrov etPierre-Brice Wieber. « A robust linear MPC approach to online generation of 3Dbiped walking motion ». In : IEEE-RAS International Conference on HumanoidRobots. 2015.

[BW17] Nestor Bohorquez et Pierre-Brice Wieber. « Adaptive step duration in bipedwalking : a robust approach to nonlinear constraints ». In : IEEE-RAS InternationalConference on Humanoid Robots. 2017.

[Car+18] Stéphane Caron, Adrien Escande, Leonardo Lanari et Bastien Mallein.« Capturability-based Analysis, Optimization and Control of 3D Bipedal Walking ».2018. url : https://hal.archives-ouvertes.fr/hal-01689331/document.

[Eng+11] Johannes Englsberger, Christian Ott, Maximo Roa, Alin Albu-Schäffer,Gerhard Hirzinger et al. « Bipedal walking control based on capture pointdynamics ». In : IEEE/RSJ International Conference on Intelligent Robots andSystems. 2011.

[Gri+17] Robert J Griffin, Georg Wiedebach, Sylvain Bertrand, Alexander Leonessa etJerry Pratt. « Walking Stabilization Using Step Timing and Location Adjustment onthe Humanoid Robot, Atlas ». In : IEEE/RSJ International Conference on IntelligentRobots and Systems. 2017.

36


references ii.

[Kaj+01a] Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kazuhito Yokoi et Hirohisa Hirukawa.« The 3D Linear Inverted Pendulum Mode : A simple modeling for a biped walkingpattern generation ». In : IEEE/RSJ International Conference on Intelligent Robotsand Systems. 2001.

[Kaj+01b] Shuuji Kajita, Kazuhito Yokoi, Muneharu Saigo et Kazuo Tanie. « Balancing aHumanoid Robot Using Backdrive Concerned Torque Control and Direct AngularMomentum Feedback ». In : IEEE International Conference on Robotics andAutomation. 2001.

[Kaj+03] Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kiyoshi Fujiwara, Kensuke Harada,Kazuhito Yokoi et Hirohisa Hirukawa. « Biped walking pattern generation by usingpreview control of zero-moment point ». In : IEEE International Conference onRobotics and Automation. 2003.

[Kaj+10] Shuuji Kajita, Mitsuharu Morisawa, Kanako Miura, Shin'ichiro Nakaoka,Kensuke Harada, Kenji Kaneko, Fumio Kanehiro et Kazuhito Yokoi. « Biped walkingstabilization based on linear inverted pendulum tracking ». In : IEEE/RSJInternational Conference on Intelligent Robots and Systems. 2010.

[Kan+11] Kenji Kaneko, Fumio Kanehiro, Mitsuharu Morisawa, Kazuhiko Akachi, Gou Miyamori,Atsushi Hayashi et Noriyuki Kanehira. « Humanoid robot HRP-4 - HumanoidRobotics Platform with Lightweight and Slim Body ». In : IEEE/RSJ International Conf.on Intelligent Robots and Systems. 2011.

37

references iii.

[Mor+12] Mitsuharu Morisawa, Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kanako Miura etKazuhiro Yokoi. « Balance control based on capture point error compensation forbiped walking on uneven terrain ». In : IEEE-RAS International Conference onHumanoid Robots. 2012.

[Nag99] Ken'ichiro Nagasaka. « Whole-body Motion Generation for a Humanoid Robot byDynamics Filters ». In : PhD thesis (1999). The University of Tokyo, in Japanese.

[Sug09] Tomomichi Sugihara. « Standing stabilizability and stepping maneuver in planarbipedalism based on the best COM-ZMP regulator ». In : IEEE InternationalConference on Robotics and Automation. 2009.

[SY17] Tomomichi Sugihara et Takanobu Yamamoto. « Foot-guided Agile Control of a BipedRobot through ZMP Manipulation ». In : IEEE/RSJ International Conference onIntelligent Robots and Systems. 2017.

[Tak+09] Toru Takenaka, Takashi Matsumoto, Takahide Yoshiike, Tadaaki Hasegawa,Shinya Shirokura, Hiroyuki Kaneko et Atsuo Orita. « Real time motion generationand control for biped robot-4th report : Integrated balance control ». In : IEEE/RSJInternational Conference on Intelligent Robots and Systems. 2009.

[Wie06] Pierre-Brice Wieber. « Trajectory free linear model predictive control for stablewalking in the presence of strong perturbations ». In : IEEE-RAS InternationalConference on Humanoid Robots. 2006.

38

walking and stair climbing stabilization for position-controlled ...hrp-4humanoidrobotinshort....

Documents