Lecture «Robot Dynamics»: Legged Robots

151-0851-00 V lecture: CAB G11 Tuesday 10:15 – 12:00, every week exercise: HG E1.2 Wednesday 8:15 – 10:00, according to schedule (about every 2nd week) office hour: LEE H303 Friday 12.15 – 13.00 Marco Hutter, Roland Siegwart, and Thomas Stastny

Case Study: Legged Robots| 1.11.2016 | 1 Topic Title 20.09.2016 Intro and Outline L1 Course Introduction; Recapitulation Position, Linear Velocity, Transformation 27.09.2016 Kinematics 1 L2 Rotation Representation; Introduction to Multi-body Kinematics 28.09.2016 Exercise 1a E1a Kinematics Modeling the ABB arm 04.10.2016 Kinematics 2 L3 Kinematics of Systems of Bodies; Jacobians 05.10.2016 Exercise 1b L3 Differential Kinematics and Jacobians of the ABB Arm 11.10.2016 Kinematics 3 L4 Kinematic Control Methods: Inverse Differential Kinematics, Inverse Kinematics; Rotation Error; Multi-task Control 12.10.2016 Exercise 1c E1b Kinematic Control of the ABB Arm 18.10.2016 Dynamics L1 L5 Multi-body Dynamics 19.10.2016 Exercise 2a E2a Dynamic Modeling of the ABB Arm 25.10.2016 Dynamics L2 L6 Dynamic Model Based Control Methods 26.10.2016 Exercise 2b E2b Dynamic Control Methods Applied to the ABB arm 01.11.2016 Legged Robots L7 Case Study and Application of Control Methods 08.11.2016 Rotorcraft 1 L8 Dynamic Modeling of Rotorcraft I 15.11.2016 Rotorcraft 2 L9 Dynamic Modeling of Rotorcraft II & Control 16.11.2016 Exercise 3 E3 Modeling and Control of Multicopter 22.11.2016 Case Studies 2 L10 Rotor Craft Case Study 29.11.2016 Fixed-wing 1 L11 Flight Dynamics; Basics of Aerodynamics; Modeling of Fixed-wing Aircraft 30.11.2016 Exercise 4 E4 Aircraft Aerodynamics / Flight performance / Model derivation 06.12.2016 Fixed-wing 2 L12 Stability, Control and Derivation of a Dynamic Model 07.12.2016 Exercise 5 E5 Fixed-wing Control and Simulation 13.12.2016 Case Studies 3 L13 Fixed-wing Case Study 20.12.2016 Summery and Outlook L14 Summery; Wrap-up; Exam Case Study: Legged Robots| 1.11.2016 | 2 Why legged robots?

. Legged systems can overcome many obstacles

. But it is quite hard to achieve this since . many DOFs must be controlled in a coordinated way . the robot must interact with (uncertain) terrain

Case Study: Legged Robots| 1.11.2016 | 3 History of Legged Robotics Walking Mechanism – First patents

. Davis, 1878 Rygg, 1893

Case Study: Legged Robots| 1.11.2016 | 4 Walking Mechanisms

1957-60 – Shigley's Walking Machines

1984 - OSU ASV (Adaptive Suspension Vehicle)

Case Study: Legged Robots| 1.11.2016 | 5 Walking Mechanism Theo Jansen

Case Study: Legged Robots| 1.11.2016 | 6 History of Legged Robotics GE Walking Truck – human controlled 4-ped

Case Study: Legged Robots| 1.11.2016 | 7 Large Scale Legged Locomotion and Manipulation

Case Study: Legged Robots| 1.11.2016 | 8 History of Legged Robotics Phony Pony, GE Hardiman and many more…

. More on http://cyberneticzoo.com/ . steam-actuated humans . mechanical elephants . …

Case Study: Legged Robots| 1.11.2016 | 9 History of Legged Robotics Humanoid robots after 2000

. Honda Asimo . Toyota Humanoid

Case Study: Legged Robots| 1.11.2016 | 10 History of Legged Robotics Humanoid robots after 2000

. Fukushima 2011 . DARPA Robotics Challenge 2012

Case Study: Legged Robots| 1.11.2016 | 11 Legged Robotics Where are we really and what are the challenges?

Case Study: Legged Robots| 1.11.2016 | 12 DARPA Robotics Challenge ... and a thing we learned after the DRC Finals

. Walking is still difficult

Case Study: Legged Robots| 1.11.2016 | 13 Static vs. Dynamic Stability

. Statically stable . Dynamic walking

. Bodyweight supported by at least three legs . The robot will fall if not continuously moving . Even if all joints ‘freeze’ instantaneously, the . Less than three legs can be in ground contact robot will not fall . fast, efficient and demanding for actuation and . Safe, slow and inefficient control

Case Study: Legged Robots| 1.11.2016 | 14 Static walking principles Inverted Pendulum

. Static walking can be represented by inverted pendulum

Case Study: Legged Robots| 1.11.2016 | 15 Static walking principles Inverted Pendulum

. Static walking can be represented by inverted pendulum . Exploit this in so-called passive dynamic walkers

Energetically very efficient

E m g hh COT  used  mg dm g dd

Case Study: Legged Robots| 1.11.2016 | 16 Static walking principles Inverted Pendulum

. Static walking can be represented by inverted pendulum . Exploit this in so-called passive dynamic walkers . Add small actuation to walk on flat ground

Cornell Ranger Total distance: 65.24 km Total time: 30:49:02 Power: 16.0 W COT: 0.28

Case Study: Legged Robots| 1.11.2016 | 17 Dynamic locomotion Leg Structure

Case Study: Legged Robots| 1.11.2016 | 18 Dynamic locomotion Leg Structure

. Leg during running is NOT and inverted pendulum . Spring loaded inverted pendulum (SLIP)  are robust against collisions  can better handle uncertainties  can temporarily store energy  reduce peak power [Alexander 1988,1990,2002,2003]

McGuigan & Wilson, 2003 – J. Exp. Bio.

Case Study: Legged Robots| 1.11.2016 | 19 Dynamic Locomotion SLIP principles in robotics

. Early Raibert hoppers (MIT leg lab) [1983] . Pneumatic piston . Hydraulic leg “angle” orientation

Case Study: Legged Robots| 1.11.2016 | 20 From Raibert Hopper to Humanoids and Quadrupeds MIT and CMU Leg Lab (1980ies)

Marc Raibert, Gill Pratt, Jerry Pratt, Hugh Herr, Russ Tedrake, Jessica Hodgins, Martin Bühler,…

Case Study: Legged Robots| 1.11.2016 | 21 From Raibert Hopper to Humanoids and Quadrupeds Boston Dynamics

. Founded 1992 . Big Dog V1 (2005), Big Dog V2 (2008)

Case Study: Legged Robots| 1.11.2016 | 22 Case Study: Legged Robots| 1.11.2016 | 23 Case Study: Legged Robots| 1.11.2016 | 24 Understanding Locomotion Summary

. Static locomotion (IP)  Dynamic Locomotion (SLIP)

. How to determine stability? . How to control (actively stabilize)?

Case Study: Legged Robots| 1.11.2016 | 25 Analyzing Stability through Limit Cycles

. Poincaré Map xxkk1  P  . Fix-Point xx** P  P . Linearization of mapping xxΦ x kkk1 x . The system is stable iff: i Φ 1

static gaits . "System is statically stable" . Does not fall if stopped

[C. David Remy, 2011] Case Study: Legged Robots| 1.11.2016 | 26 Dynamic Locomotion Stability Analysis

x . Point mass: q    y . Equation of Motion: . flight x0  q    yg 

x . stance  Fspring    xm q  o    y  y F  spring g  mo 

Fspring  fkl ,, Case Study: Legged Robots| 1.11.2016 | 27 Stability of Locomotion Limit Cycle Analysis

x . Point mass: q    y . Equation of Motion: . flight x0  q    yg 

x . stance  Fspring    xm q  o    y  y F  spring g  mo 

Fspring  fkl ,, Case Study: Legged Robots| 1.11.2016 | 28 Stability of Locomotion Limit Cycle Analysis

x zk zk1 . Point mass: q    y . System state

x analysis at   y apex y z  z    x x     y . How does the state propagate from one apex to the next?

Case Study: Legged Robots| 1.11.2016 | 29 Stability of Locomotion Limit Cycle Analysis

. Given the Poincaré mapping from one apex to the next zzkk1  P  . P includes differential equations that cannot be analytically solved!

. Analyze periodic stability of a fixed point zz** P 

. How can we do this? Linearization… 0 2 ***PP 2 zzzkk11PP zz  k z   zk2  z k... *  x xx x xx * z* P zzΦ z kkk1 z

? Case Study: Legged Robots| 1.11.2016 | 30 Stability of Locomotion Numerical Limit Cycle Analysis

yykk1 P  . Find the linearization of the Poincaré map around fix-point   * xkk1 x xx x

yk 1 . Choose  z k     h , with a small h xk 0 y 1 k 1 Phz* . Simulate until the next apex, starting from    * xk 1 0 yyk 1  * P h . Calculate   * x * xx xx k 1 * h y 0 . Do the same thing for k zk    h xk  1

Case Study: Legged Robots| 1.11.2016 | 31 Stability of Locomotion Numerical Limit Cycle Analysis

P . The previous evaluation results in a 2x2 matrix x * . Eigenvalue analysis: xx . System is energy conservative: 1  1 . System can be . stable 2  1 . unstable: 2  1

Case Study: Legged Robots| 1.11.2016 | 32 Stability and Control of Locomotion Example of a biped

. External disturbances lead to instability

[Coros 2012]

Case Study: Legged Robots| 1.11.2016 | 33 Stability and Control of Locomotion Example of a biped

. External disturbances lead to instability . Foot step control for fall recovery

[Coros 2012]

Case Study: Legged Robots| 1.11.2016 | 34 Legged Robots for Challenging Environments

Marco Hutter Robotic Systems Lab, ETH Zurich 28.10.2016

Case Study: Legged Robots| 1.11.2016 | 41 Legged Robots for Challenging Environments

. Macerata, 2 days ago

| | Legged Robotics Research at ETH

2009 2012 2015

ALoF StarlETH ANYmal

| | ALOF a versatile quadruped robot

. High mobility . Clever design . Precise kinematic planning

| | How to engineer a dog

| | Case Study: Legged Robots| 1.11.2016 | 46 Biomechanics of Animals Compliance in muscles and tendons

. Muscle/tendon (mech. compliance) . Robustness . Energy storage . Power/speed amplification . Force control instead of position [Alexander 1988,1990,2002,2003]

Case Study: Legged Robots| 1.11.2016 | 47 From Position to Force Controlled Systems Compliance in robotic actuation

. Kinematic, position control position

motor gear link

. Dynamic, force control position force

motor gear spring link

Case Study: Legged Robots| 1.11.2016 | 48 High-performance Series Elastic Actuators Driving dynamic robots

. How to . … select the optimal compliance? . … mechanically integrate this compliance? . … optimally exploit the compliance? . … control systems with integrated compliance?

StarlETH ANYmal

Case Study: Legged Robots| 1.11.2016 | 49 StarlETH A compliant quadrupedal robot

Case Study: Legged Robots| 1.11.2016 | 50 [Gehring et. al., ICRA 2013, RAM 2015] StarlETH – a Compliant Quadrupedal Robot Towards autonomous running and climbing

Case Study: Legged Robots| 1.11.2016 | 51 [Hutter et. al., TMECH 2011, TRO 2014] Exploitation of Passive Dynamics

. 64% passive energy recovery [Roberts 2002] . Speed amplification 4.7, power amplification 4.1

position power

motor gear spring link

Case Study: Legged Robots| 1.11.2016 | 52 ANYdrive A robust and force controllable robot joint unit

. Fully integrate SEAs . Custom motor control and sensing (no communication delay) m=870g . CAN (future EtherCAT) and power interface . Precise absolute output position and torque control . Hollow shaft for cabling . Large output load bearing . IP67

93mm

80mm

Case Study: Legged Robots| 1.11.2016 | 53 ANYdrive Setup Position encoder Output bearing RLS AksIM Double row angular Motor electronics Custom

Brushless motor Robodrive ILM

Titanium spring Custom Sealed aluminium housing Harmonic Drive gear Custom

Case Study: Legged Robots| 1.11.2016 | 54 Case Study: Legged Robots| 1.11.2016 | 55 ANYmal – System overview

. High mobility . Extensive range of motion . Various maneuvers (climb)

. Powerful, dynamic & efficient . Different gaits (walk, trot, jump,…)

Case Study: Legged Robots| 1.11.2016 | 56 [Fankhauser et. al., 2016] ANYmal Combining dynamic motion skills with large mobility

Case Study: Legged Robots| 1.11.2016 | 57 ANYmal – System overview

. Fully autonomous . Onboard localization, mapping, planning, and control . Modular sensor payload

. Field-ready . Water-proof . 2–3 h endurance (280W avg power) . 1-person operation (30kg) . GUI for intuitive tele-operation . Fall-safe

Case Study: Legged Robots| 1.11.2016 | 58 Software and Electronics Architecture

12× ANYdrive IMU 4× Foot contact 2× Laser range 2× Wide-angle Zoom camera 2× Microphone Industrial sensor sensor camera Thermal cameraVisible & IR light Wireless Operator PC

WiFi Wireless Router Remote control UI Locomotion PC Navigation PC Inspection PC Manual, supervised control Localization Visualizations RT ICP, Rovio, Tango etc. Sensors, robot state, environment State estimation Visual inspection Gauges, levers Legged odometry, ground est. Terrain mapping Mission Elevation mapping, traversability est. Mission creating and protocol Locomotion Control Thermal inspection Motion planning Trotting, crawling, Free Gait Ethernet Navigation, foothold selection Audio inspection Pump & alarm sounds Radio ROS interface Mission execution

Safety operator

Case Study: Legged Robots| 1.11.2016 | 59 Locomotion

State Estimation Whole-Body Control Actuation Robot Joint torques Robot state Joint commands Sensor measurements Sensor

Case Study: Legged Robots| 1.11.2016 | 60 State Estimation

Inertial measurements External pose Extended Kalman Filter measurements . No assumption on terrain . Kinematic measurements (encoders) for legs in contact . Fused with inertial measurements (IMU) . Error < 5% over distance . Optionally combined with external pose (GPS, laser, vision, etc.)

Kinematic measurements

M. Bloesch, C. Gehring, P. Fankhauser, M. Hutter, M. A. Hoepflinger and R. Siegwart, “State Estimation for Legged Robots on Unstable and Slippery Terrain”, in International Conference on Intelligent Robots and Systems (IROS), 2013.

Case Study: Legged Robots| 1.11.2016 | 61 Locomotion

State Estimation Whole-Body Control Actuation Robot Joint torques Robot state Joint commands Sensor measurements Sensor

Case Study: Legged Robots| 1.11.2016 | 62 Foot Placement Control Balance from stepping

. Biomechanical studies suggest SLIP models to describe complex running behaviors

[Dickinson, Farley, Full 2000] [Geyer 2006]

1 FB rrF HC,, desTk st R r HC des  r HCh HC [Raibert 1986] . Simple step-length rule to adjust the velocity 2

Constant speed Accelerate Decelerate

Case Study: Legged Robots| 1.11.2016 | 63 Foot Placement Control Balance from stepping

Case Study: Legged Robots| 1.11.2016 | 64 Kinematics and Dynamics in Control Inverse kinematics for swing leg control estimated base configuration

. Foot point in base frame χˆˆˆBOBRB r ,χ ,

rBF, des rOF, des rˆOB

. Expressed in world frame IBFrrq IBF r,χ B . Expressed in body frame B rrqBF B BF r 

. => inverse kinematics in body frame

BBFdesr ,,R BIχˆˆ R, B IOFdr , es B rOB BBFderqs  r,swingeg l  {I} planned swing leg trajectory

IOFdesr , t

| | Whole-body Control of a Legged Robot

causes motion actuation inverse dynamics TT . Equations of motion Mq  b g Jss F  S τ contact force . Contact constraint  Jqss Jq   0

min r qr or rr  . Desired motion optimization i des 2 i i,max

min WF bFF or . Contact force optimization s s Fs2 si ,max

minW τ b or τ τ . Joint torque optimization   2 max

Whole-body control = large scale simultaneous optimization of q, Fs , τ

Case Study: Legged Robots| 1.11.2016 | 66 Kinematics and Dynamics in Control (simple) whole body control estimated base configuration

. Adjust joint torques to χˆˆˆBOBRB r ,χ ,     . track the swing leg rJqJOFF Fq rOF, des ()t target base configuration wJqJ   q  w ()t . to move the base BB B Bd, es χBdes,,,()ttt r OBdes (),χ RBdes, ()

 . ensure contact constraint rJqJq0cc  c 

 fully defines the motion of the system 12 actuated + 6 unactuated = 18 DOF 6 motion + 9 constraints + 3 swing leg = 18 {I} planned swing leg trajectory If more tasks, 1  use pseudo-inverse JJFFrOF (t)     IOFdesr , t qJ w (t) Jq  des B B  B   JJc 0  c     ˆˆˆˆTT T . Inverse dynamics control τ  NSccdes N Mq  b gˆ

| | Locomotion as Optimization Problem

. Write inverse dynamics as constraint (prioritized) optimization

 . Step 1: move base min w B,des (t) J BqJ Bq  q T <= equation of motion holds s.t. Mq  b g Jcc F  S τ  JqBB Jq   0 <= contact constraint holds F  F cn,,mini n <= minimal normal contact force FF cn,,ii ct 2 <= contact force in friction cone  min rOF, des (t) J FFq J q . Step 2: move swing leg q ct x () JJq  q  1,Bdes BB <= higher priority task is not influenced s.t.  T Mq b g Jcc F  S τ <= equation of motion holds F  F cn,,mini n <= minimal normal contact force FF cn,,ii ct 2 <= contact force in friction cone

min τ min F . Last step: minimize e.g torque or tangential contact forces s,ti s.t. all other task are still fulfilled

| | Static Walking with Compliant Behavior

| | Static Walking – Force/Torque Optimization

. Different force and torque optimization strategies:

. Reduced energy consumption by torque minimization WI 

. Reduction of risk of slippage by contact force alignment WF  diag ti 

20%

[Hutter et al, RSS 2012, IJRR 2014]

| | Static Walking – Force/Torque Optimization

. Different force and torque optimization strategies:

. Reduced energy consumption by torque minimization WI 

. Reduction of risk of slippage by contact force alignment WF  diag ti 

| | Joint Torque Limitations

. Inequality tasks

| | Joint Position Limitation

. Base shifting . Joint Limitation = Inequality constraint

| | Task Prioritization (Bellicoso, Humanoids 2016)

| | [Gehring et. al., ICRA, 2013] Motion Synthesis from Optimization

. Parameterization of behavior Target behavior = cost function optimizer . Motion primitives CMA-ES, . Gait pattern ROCK*,   θ θθargminwCii ,,,qqτ . Control gains PI2, … θ . …

Case Study: Legged Robots| 1.11.2016 | 75 Motion Synthesis from Optimization

[Geijtenbeek et. al., 2013]

Case Study: Legged Robots| 1.11.2016 | 76 Emerging Behaviors High jumping manoeuver

. Model ENTIRE system (including actuator dynamics and mechanical elasticity) allows reaching maximum performance

Case Study: Legged Robots| 1.11.2016 | 77 ANYmal – Application in real-world scenarios

. ARGOS challenge . NCCR rescue robotics . Autonomous inspection of oil and gas sites . S&R application together with UAVs

Case Study: Legged Robots| 1.11.2016 | 78 ARGOS Challenge Autonomous Inspection of Oil and Gas Sites

Case Study: Legged Robots| 1.11.2016 | 79 ARGOS Challenge Autonomous Inspection of Oil and Gas Sites

Mission planning Mission layout, decision making, user interface …

Inspection Gauges, water levels, levers, heat sources, alarm sounds … Navigation Path planning, localization, obstacle avoidance … Climbing Steps, Pipes, Stairs …

Case Study: Legged Robots| 1.11.2016 | 80 ARGOS Challenge 5 International Teams (Industry + Academia)

AIR-K ARGONAUTS Japan Austria & Germany

LIO Switzerland FOXIRIS VIKINGS Spain & Portugal France

Case Study: Legged Robots| 1.11.2016 | 81 Locomotion Control

Locomotion Controller Modules (Loco) Robot Controller Manager (Rocoma) Controller Layer Virtual model Pose Reflexes control optimization Trotting Crawling Free Gait … Trajectory Whole-Body Gait optimization Control patterns First Emergency Emergency Emergency Zero-Moment Contact force Controller A Controller B … Layer Point Traj. distribution Second Fail-proof Emergency Controller Layer

C. Gehring, S. Coros, M. Hutter, D. Bellicoso, H. Heijnen, R. Diethelm, M. Bloesch, C. Dario Bellicoso, C. Gehring, J. Hwangbo, P. Fankhauser, M. Hutter, “Emerging P. Fankhauser, J. Hwangbo, M. A. Hoepflinger, and R. Siegwart, “Practice Makes Terrain Adaptation from Hierarchical Whole Body Control,” Perfect: An Optimization-Based Approach to Controlling Agile Motions for a in IEEE Internal Conference on Humanoid Robots (Humanoids), 2016. Quadruped Robot.”, in IEEE Robotics & Automation Magazine, 2016.

Case Study: Legged Robots| 1.11.2016 | 82 Navigation

Laser Range Data Localization Elevation Mapping

Traversability Est. Navigation Planning Execution

Case Study: Legged Robots| 1.11.2016 | 83 [Diethelm et. al., 2015] Navigation ICP Localization

. Point cloud registration for localization in reference map . Full rotation of LiDAR is aggregated for point cloud . Use of existing maps or online mapping

Case Study: Legged Robots| 1.11.2016 | 84 Navigation Elevation Mapping – Dense Terrain Mapping

. Probabilistic fusion of range measurements and pose estimation

. Explicitly handles drift of state estimation (robot-centric)

. Input data from laser, Kinect, stereo cameras, Velodyne etc.

P. Fankhauser, M. Bloesch, C. Gehring, M. Hutter, R. Siegwart “Robot-Centric Elevation Mapping with Uncertainty Estimates,” in International Conference on Climbing and Walking Robots (CLAWAR), 2014.

Case Study: Legged Robots| 1.11.2016 | 85 Navigation Traversability estimation

Slope

Roughness ∑

Elevation map Traversability map

Step height Not Fully traversable traversable M. Wermelinger, P. Fankhauser, R. Diethelm, P. Krüsi, R. Siegwart, M. Hutter, “Navigation 01 Planning for Legged Robots in Challenging Terrain,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016.

Case Study: Legged Robots| 1.11.2016 | 86 Navigation Planning

. Online navigation planning based on RRT* (OMPL)

. Works with and without initial map

. Continuous for changing environments

M. Wermelinger, P. Fankhauser, R. Diethelm, P. Krüsi, R. Siegwart, M. Hutter, “Navigation Planning for Legged Robots in Challenging Terrain,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016.

Case Study: Legged Robots| 1.11.2016 | 87 Collaborative Navigation Vision based localization

| | Inspection

Visual inspection Thermal Inspection Auditive Inspection

Pressure & Level gauges Valves Thermal points Pumps Gas leaks Platform alarm

Zoom-camera Thermal- Microphones (audible and ultra-sonic) (visible & IR) camera

Case Study: Legged Robots| 1.11.2016 | 90 Inspection Visual inspection of pressure gauges Automatic view point generation Visual servoing Indicator reading

➔ Reading ok Whole-body camera positioning Image de-warping

➔ Reading unsuccessful, try alternative position or report as unknown S. Bachmann, “Visual Inspection of Manometers and Valve Levers”, Master’s Thesis, ETH Zurich, 2015.

Case Study: Legged Robots| 1.11.2016 | 91