Walking and stair climbing controller for locomotion in an aircraft - PowerPoint PPT Presentation

Walking and stair climbing controller for locomotion in an aircraft factory by the HRP-4 humanoid robot . Stéphane Caron June 5, 2019 Talk given at the NASA-Caltech Jet Propulsion Laboratory

motor intelligence 1

historical parallel . Chess : • 1956 : simplified rules, beats novice • 1967 : full rules, wins tournament • 1981 : beats master in tournament • 1997 : beats world champion 2

historical parallel (cont’d) . Robot Soccer World Cup (Robocup) « ... to develop a team of humanoid robots that is able to win against the official human World Soccer Champion team until 2050. » • Established in 1996 • Still simplified rules in 2019 • Yearly update towards human rules 3

honda p2 humanoid robot . Public demonstration in 1998 : • Zero-tilting Moment Point (ZMP) control • Ground reaction force control • Impact absorption (SEA before SEA) : 1 1. Kazuo Hirai, Masato Hirose, Yuji Haikawa et Toru Takenaka. « The development of Honda hu- 4 manoid robot ». In : IEEE International Conference on Robotics and Automation . 1998.

kawada hrp-4 humanoid robot . Stiff position control on all joints Mechanical flexibility at the ankles 2 2. Kenji Kaneko, Fumio Kanehiro, Mitsuharu Morisawa, Kazuhiko Akachi, Gou Miyamori, Atsushi Hayashi et Noriyuki Kanehira. « Humanoid robot HRP-4 - Humanoid Robotics Platform with Light- 5 weight and Slim Body ». In : IEEE/RSJ International Conf. on Intelligent Robots and Systems . 2011.

on-site demo at airbus saint-nazaire . Figure 1 : Locomotion, balancing and manipulation to achieve the use case 6

system overview . Source code : https://github.com/stephane-caron/lipm_walking_controller/ 7 Whole-body Walking Whole-body Kinematic Pattern Admittance Control Generation Control DCM DCM Control Observer

physics : from simple to complex .

point mass dynamics . Newton's second law • m : total mass • c : center of mass (CoM) • g : acceleration due to gravity • F : external force 8 m ¨ c = mg + F

rigid body dynamics . Newton-Euler equations (2D) • I : moment of inertia around the CoM • p : contact point • F : external force 9 m ¨ c = mg + F I ¨ θ = ( p − c ) × F • ˙ θ : angular velocity around the CoM

articulated body dynamics . Equation of motion • n : number of actuated joints • G : gravity and nonlinear effects • J : contact Jacobian • F : external forces 10 M ¨ q = G + S T τ + J T F • q : generalized coordinates ( n + 6) • M : inertia matrix ( n + 6) 2 • τ : actuated joint torques

control : from complex to simple .

task function approach . Figure 2 : Control task targets rather than generalized coordinates 11

centroidal dynamics . 3. David E. Orin, Ambarish Goswami et Sung-Hee Lee. « Centroidal dynamics of a humanoid ro- 3 12 motion reduces to Newton-Euler again : Equation of motion If motors can produce τ ∈ R n , equation of m ¨ c = mg + ∑ i F i ˙ L c = ∑ i ( p i − c ) × F i • L c : angular momentum around c • p i : application point of force F i bot ». In : Autonomous Robots 35.2 (oct. 2013).

choice of angular momentum . Figure 3 : Net contact force does not go and translates Figure 4 : Net contact force goes through rotation Bottom line A constant angular momentum reduces the system to translation 13 through CoM ⇒ ˙ L = I ¨ CoM ⇒ ˙ θ > 0 , body rotates L = 0 , body translates only, no

zero-tilting moment point the net contact force is applied. (2004). 4. P. Sardain et G. Bessonnet. « Forces acting on a biped robot. center of pressure-zero moment 4 contact surface at the CoP. . • Formally : the ZMP axis intersects the • Informally : the ZMP is the point where wrench is aligned with the contact normal n . Point s Z where the moment of the contact Zero-tilting Moment Point (ZMP) Point C on the contact surface where the Center of pressure (CoP) 14 resultant of pressure forces F p is applied. E ff ect of Angular Momentum point ». In : IEEE Transactions on Systems, Man and Cybernetics, Part A : Systems and Humans 34.5

linear inverted pendulum mode . Equation of motion • p : zero-tilting moment point (ZMP) 5 5. Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kazuhito Yokoi et Hirohisa Hirukawa. « The 3D IEEE/RSJ International Conference on Intelligent Robots and Systems . 2001. 15 • Constant angular momentum ˙ L c = 0 • Constant CoM height c z = h c = ω 2 ( c − p ) ¨ • ω 2 = g / h is a constant Linear Inverted Pendulum Mode : A simple modeling for a biped walking pattern generation ». In :

comparison to a classical example . Equation of motion x is a discrete action • x is unconstrained Equation of motion • p is a hybrid continuous action • p is constrained to the foot sole 16 θ ≈ ω 2 ( θ − p ) ¨ c = ω 2 ( c − p ) ¨ • p ∝ ¨ • θ may go down to ± π • c may diverge to ±∞

divergent component of motion . Conference on Intelligent Robots and Systems . 2009. 6. Toru Takenaka, Takashi Matsumoto et Takahide Yoshiike. « Real time motion generation and 6 • Boundedness condition [LHM14] linear feedback controllers [Sug09] • Maximizes basin of attraction among 17 Equation of motion c • Divergent component of motion : • Linear inverted pendulum mode : c = ω 2 ( c − p ) ¨ ξ := c + ˙ ω ˙ ξ = ω ( ξ − p ) control for biped robot-1st report : Walking gait pattern generation ». In : IEEE/RSJ International

Walking pattern generation .

linear model predictive control . Cost function • Track desired ZMP reference • Track desired CoM velocity • Minimize CoM jerk Constraints • Consistency : equation of motion • Feasibility : ZMP in support area • Viability : terminal DCM 7 7. Pierre-Brice Wieber. « Trajectory free linear model predictive control for stable walking in the 2006. 18 presence of strong perturbations ». In : IEEE-RAS International Conference on Humanoid Robots .

linear model predictive control (quadratic program) N 2006. 8. Pierre-Brice Wieber. « Trajectory free linear model predictive control for stable walking in the 8 ... ... . N 19 min ... w z N ∥ p [ k ] − p d [ k ] ∥ 2 + w v c d [ k ] ∥ 2 + w j c [ k ] ∥ 2 ∑ ∑ ∥ ˙ c [ k ] − ˙ ∑ ∥ ... c [1 ... N ] k =1 k =1 k =1 c [ k ] + T 2 c [ k ] + T 3 c [ k + 1] = c [ k ] + T ˙ 2 ¨ s . t . ∀ k c [ k ] 6 c [ k ] + T 2 ˙ c [ k + 1] = ˙ c [ k ] + T ¨ c [ k ] 2 ¨ c [ k + 1] = ¨ c [ k ] + T ... c [ k ] Equation of motion : p [ k ] = c [ k ] − ¨ c [ k ] ω 2 Feasibility : p min [ k ] ≤ p [ k ] ≤ p max [ k ] Viability : c [ N ] + ˙ c [ N ] = ξ d [ N ] ω presence of strong perturbations ». In : IEEE-RAS International Conference on Humanoid Robots .

visualization . Figure 5 : Stair climbing motion in mc_rtc 20

Walking stabilization .

role of stabilization . Actuated joints converge but unactuated floating base diverges : Planned motion On robot without stabilization 21

visualization . Figure 6 : Standing stabilization under external forces 22

let us review the facts . • The floating base is unactuated • We can control it via the CoM and Newton-Euler equations • In the LIPM, they are reduced to : • Feedback is realized by indirect force control of the ZMP : • Best control is by DCM feedback : 23 c = ω 2 ( c − p ) ¨ p = p d − k p ( c d − c ) − k d (˙ c d − ˙ c ) p = p d − k ( ξ d − ξ )

indirect force control . ... but our robot is position-controlled ? Split control into two components : Admittance control Change position targets in order to track desired forces DCM feedback control Assuming force control, decide reaction forces that drive the floating base 24

admittance control strategies . Admittance control strategies for different components of the net contact wrench : • CoP at each contact [Kaj+01b] • Pressure distribution [Kaj+10] • CoM admittance control [Nag99] 25

center-of-pressure control . • Rotate end-effector to move its CoP • Assumes compliance at contact : • Apply damping control : Figure adapted from [Kaj+01b] 9 9. Shuuji Kajita, Kazuhito Yokoi, Muneharu Saigo et Kazuo Tanie. « Balancing a Humanoid Robot Using Backdrive Concerned Torque Control and Direct Angular Momentum Feedback ». In : IEEE International Conference on Robotics and Automation . 2001. 26 τ = K e ( θ − θ e ) ˙ θ = A cop ( τ d − τ ) • Closed-loop behavior has τ → τ d

pressure distribution control . Kaneko, Fumio Kanehiro et Kazuhito Yokoi. « Biped walking stabilization based on linear inverted 10. Shuuji Kajita, Mitsuharu Morisawa, Kanako Miura, Shin'ichiro Nakaoka, Kensuke Harada, Kenji 10 Figure adapted from [Kaj+10] 27 • Apply damping control : • Push down with foot that needs more • Net vertical force compensates pressure, lift the other one gravity ⇒ only need to control : ∆ f z = f Rz − f Lz * d z p * d ctrl p Lz Rz ˙ z ctrl = A z (∆ f zd − ∆ f z ) f f Rz Lz pendulum tracking ». In : IEEE/RSJ International Conference on Intelligent Robots and Systems . 2010.