SBRML Part5 Introduction to Bipedal Walking · 2 Sensor Based Robotic Manipulation and Locomotion...

1 Sensor Based Robotic Manipulation and Locomotion

Introduction to Bipedal Walking

Dr.-Ing. Christian OttDLR - Institute for Robotics and Mechatronics

For full lecture on humanoid systems see Christian‘s lecture at EIModeling and Control of Humanoid Walking Robots

http://www.robotic.dlr.de/chr

DLR 02/05/2012

Motivation

Honda Asimo

Bipedalism:• Stepping on different heights and over obstacles• Small region of support compared to wheeled robots• Humanoid body structure allows to act

in human environments• Smallest number of legs required for

standing, walking, running• Fundamental research:

Control, planning, mech. designUnderstanding (human) balance

• „Technological competition“: Sony, Honda, Toyota, Samsung,Aldebaran, Boston Dynamics, …

• …

Humanoid Balance

Vestibular system

Vision

Somatosensory System

Proprioceptivesensors

Vision

force sensors

joint sensing

“Balance” is a generic term describing the ability to control the body posturein order to prevent falling.

Humanoid Balance

Small push:Ankle strategy

force controlZMP control

(Zero Moment Point)

angular momentum control

Medium push:Hip strategy

Large Push: Step strategy

Strategies for human push recovery:

Balancing Walking

Types of bipedal gaitStatic walking: Ground projection of center of motion (COM) never leaves support polygon

Dynamic walking:Def A: Ground projection leaves support polygon during motion„Def B: Walking with underactuation“ (e.g. point foot walking)

Running: includes flight phase

Models

Multi-Body-Models Conceptual Models

Fixed Base Models(predefined contact state)

Floating Base Model Walking Running

Dynamical Models (Mechanical)

Complexity

Specialization

Floating base model

)3(SEHb Qq

111 SSST n

Configuration Space: )3(SEQ

Using local coordinates: n6

Free-Floating vs. Fixed Base Models

Fixed base modelsIn each contact state the model is different:

• Single support (right, left)• Double support• Heel Off• Toe Touch Down• …

Transition between contact states

double supportparallel kinematicsover-constrained

need for passive joints

single supportserial kin. chainor tree structure

Free-floating model

Components:• Lagrangian dynamics• Constraints due to contact forces• Transition equations (impacts)

underactuated

Planning & control must ensure that the considered contact state is valid! ground reaction force must fulfill constraints for balancing

Zero Moment Point[Vukobratovic and Stepanenko,1972]

)(x1x 2x

ZMP as a ground reference point: Distributed ground reaction force under the supporting foot can be replaced by a single force F acting at the ZMP, called ground reaction force.

),( yx

ZMP = CoP (Center of Pressure)

p1x 2x

Definition of the Zero Moment Point (ZMP)

Planar single support:

Distributed floor reaction force under the supporting foot can be replaced by a single force acting at the ZMP.

[Vukobratovic and Stepanenko,1972]

)(0)( x

dxxxpp

)(x1x 2x

210)( xpxx

)()()(x

xdxxpxp

ZMP = CoP (Center of Pressure)

Extension to two dimensions is straight forward

Some facts about the ZMP• Can ZMP leave the support polygon? NO• Can ZMP location be used as a stability criterion NO

• If ZMP reaches the border of the support polygon foot rotation possible.

• ZMP is defined on flat contact (no uneven surface).• ZMP gives no information about sliding.

)(x1x 2x

Measurement e.g. by Force/Torque Sensor

),,(0)()(!

ssssss fppfppp

How to obtain ZMP in practice?

First usage of the ZMP• Motion of the legs is predefined.• Upper body controls the ZMP in the center of the supporting foot

ensure proper foot contact during walking

Conceptual Models for Walking

Cart table model Inverted pendulum model

Ground reaction force should stay within the stance area

Ground reaction force stays at the hinge point of the pendulum

Can be derived from the general model:

• Approximation of angular momentum

• Limited motion (no vertical COM motion)

Basis for many successful walking robots

NAO HRP-2 ASIMO

Mass Concentrated Model for Linear Inverted Pendulum

Forces in the linear inverted pendulum (LIP) model

pccgc xz

pf p p

mass concentrated model

Forces in the LIP model

Effect of an additional hip torque

pccgc xz

x Mcpc

mass concentrated model

Strategies for gait stabilization: Effect of an additional hip torque

x Mcpc

1. Controlling ZMP (constraints!)

2. Angular momentum control

3. Step adaptation

Mass concentrated model for ZMP Control

gcccp xz

xcInverted Pendulum Model [Sugihara]

x pccgc

xx pc xx cp

Cart Table Model [Kajita]

Simplifying assumptions• robot mass concentrated in the center of mass (CoM)• CoM height cz is kept constant

We have a simple relation between the motion of the CoM and the ZMP

ZMP based walking pattern: basic scheme

Footstep planning

Walking Pattern

Generator

CoM Inverse

kinematics

Joint Position Control

dp dc dq

Image copied without explicit permission from Workshop material “Overview of ZMP-based Biped Walking” at Dynamic Walking conference 2008, by S. Kajita.

Simple solution: Use hip motion (+offset) instead of CoM

Here, CoM is controlled

DLR Robot Control Based on Conceptual Models

Footstep Generation

Pattern Generation

pZMP-COMStabilizer

dxPos. Controlled

e.g. LQR Preview Control [Kajita, 2003]

Model Predictive Control [Wieber, 2006]

realtime

Automatica 2010

ZMP is controlled

Torque Based BalancingA Unified Approach for

Grasping and Balancing

Torque based balancingAssumptions:

Joint Torque Control

COM and hip orientation can be measured in a world-fixed frame (via inertia measurement unit – IMU - measurement)

extFMg

Control Approach:

1. Compute desired force on the COM (according to compliant behavior)

extFMg

Control Approach:

1. Compute desired force on the COM(according to compliant behavior)

2. Distribute COM force to contact points COMF

extFMg

COM and hip orientation can be measured in a world-fixed frame (via IMU measurement)

Control Approach:

1. Compute desired force on the COM(according to compliant behavior)

2. Distribute COM force to contact points

3. Realize contact forces via joint torques

extFMg

Force distribution: grasping and balancing are very similar problems!

Grasping and Balancing

Force Distribution in Grasping

FGGFGFGWO

111Net wrench acting on the object:

Grasp Map

)3(seFC

Well studied problem in grasping: Find contact wrenches such that a desired net wrench on the object is achieved.

friction cone

Balancing & Posture Control

Compliant COM control [Hyon & Cheng, 2006]

Compliant trunk orientation Control =>

)()( dDdPCOM ccKccKMgF

)3(SOR

HIPT extT

),( HIPCOMd TFW Desired wrench:

Quaternion based orientation compliance control(see passivity based Cartesian impedance control)

Force distribution

Relation between balancing wrench & contact forces

Constraints:• Unilateral contact: (implicit handling of ZMP constraints)• Friction cone constraints

0, zif

Force distribution

Relation between balancing wrench & contact forces

Constraints:• Unilateral contact: (implicit handling of ZMP constraints)• Friction cone constraints

0, zif

Formulation as a constraint optimization problem

21minarg CCTHIPCFCOMC ffGTfGFf

ForceDistribution

Torque based balancing

Force Mapping

TorqueControl

RobotDynamics

Object ForceGeneration

for orientation control and COM computation

ForceDistribution

Torque based balancing

Force Mapping

TorqueControl

RobotDynamics

Object ForceGeneration

for orientation control and COM computation

Contact forces

Summary

1. Consistent treatment of COM and posture control (useful for manipulation, bipedal vehicles)

2. Implicit handling of ZMP via constraints in the force optimization

3. Utilizes a formulation from grasping theory: Allows for generalization to multi-contact situations

4. Controller is independent of precise knowledge about foot contact(however, IMU data is important!)

Outlook:- Extension to multi-contact interactions- Extension to walking

Overview

1. Fundamentals about bipedal walking

2. Time based walking control ZMP based control

3. Limit cycle based walking Passive dynamic walking

Passive Dynamic Walking„Passive Dynamic Walking“

Dynamics Control

• Careful mechanic design:knee retraction, foot shape, trunk, elastic elements

• Analysis: Limit cycle (Poincare Map), impacts

Passive Dynamic Walking

„Dynamic Walking“

Actuation + Dynamics

„Passive Dynamic Walking“

Dynamics Control

Conceptual Models: RunningTemplates

• Template for control

• Template for design

[Geyer, Seyfarth, Blikhan, 2006]

Role of compliance for human walking/running.

[Oscar Pistorius][A. Sato, Mc Gill Univ.]

Legged Hopping Robots

[Raibert, MIT]

Three part control:

1. control of hopping height (during stance)

2. control forward velocity via foot positioning

3. control of body orientation by servoing the hip

[Raibert, MIT]

That's all Folks!

SBRML Part5 Introduction to Bipedal Walking · 2 Sensor Based Robotic Manipulation and Locomotion...

Documents

Skeletal Features of Bipedalism - Los Angeles Harbor College Anthro-Skeletal... · 2010-04-30 · Skeletal Features of Bipedalism • Foramen magnum: Latin, “large hole”, cranial

Mengenal Seluk Beluk Asimo

Robot Asimo

Bipedalism - Mr. Brown's Webpageheritagesocialstudies.weebly.com/.../54074601/bipedalism.pdf · 2019-10-02 · bipedalism are seen in early hominid fossils. • Some researchers believe

Japanese robot honda asimo

Models on WHY? Why we became bipedal (6 hypotheses)6 hypotheses Efficient bipedalism as the primary form of locomotion is seen only in hominins

Thesis.fi.En Bipedal Model

Key Trends in Hominid evolution. Bipedalism is walking on two legs. First observed in Australopithecines Adaptations of the human body for bipedal locomotion

BIPEDAL LOCOMOTION Antonio D'Angelo. BIPEDAL WALKING In recent years the interest to study the bipedal walking has been growing. Also the demand for build

Origins Obligate Bipedal Ism

Bipedalism - Maxwell Museum of Anthropology 2.… · Bipedalism . One of the earliest traits that our human ancestors developed was the ability to walk upright – bipedalism. This

Design and Evaluation of an Active Artificial Spine in a ... · bipedal locomotion. Despite the bipedalism ability, Charlie has to perform a posture transition, from a four-legged

ASIMO(FAITH FOSTER).ppt

AJLONTECH design.pdf · Who is ASIMO? ASIMO is a humanoid robot created in 2000 by Honda. ASIMO stands for Advanced Step in Innovative MObility 11th in line of successive bipedal

ON CONTROLLABLE STIFFNESS BIPEDAL WALKING · the heel-strike and the foot-touch-down in bipedal walking) demonstrate signiﬁcant improvements in the energetics of the bipedal walking

04. Bipedal Walking Robot Ok

TF(ESCENARIOS-FAR) ASIMO

Advantage Bipedalism & Food Transport

step by step: the evolution of bipedalism

honda asimo