Whitman and Atkeson

Present a decoupled controller for a simulated three-dimensional biped. Dynamics broke down into multiple

subsystems that are controlled seperately.

Policies are brought back into simplified states and control action back onto the full system.

2Cognitive Robotics 2010

Coordination of multiple policies: Time till touch down

Dynamic programming simultaneously and globally optimize: Foot placement Step timing Body motion

3Cognitive Robotics 2010

Paradigm: high degree of freedom (DoF) systems generate a nominal trajectory stabilized with a feedback controller. Only functions in a small tube or within the

state space.

Produce policies that are valid for a large region of the state space (Brice et. al. 2006) Library of multiple trajectories.

4Cognitive Robotics 2010

Dynamically stable walking trajectories based on the zero moment point (ZMP).

A desired ZMP trajectory was chosen before the specified footstep locations and timing. Then the CoM trajectory is calculated based on the desired ZMP trajectory. Kajita et. al. (2006)

5Cognitive Robotics 2010

State space (1) Pick a new action, best or random. (2) Update the value function.

Compass gait walker Point mass on two rigid legs.

6Cognitive Robotics 2010

Five rigid legsW: 78 kg (50 torso, 14 legs)Length; Legs: 0,81 mCoM: 1,00 m above ground12 DoF

6 torso; 2 x 2 for hip and 1 for each knee.

3 Pitch joints for ankle. u = coefficient of friction = 1,0

7Cognitive Robotics 2010

High dimensional state/action spaceLower dimensional:

Each joint in sagittal/coronal plane. ▪ Dynamics decoupled and control separately.▪ Left and right coupling at the same time.▪ Double support is ignored (1% - 2% step)

because compass gait.

8Cognitive Robotics 2010

7 DoF 3 on the torso 4 on the hip and knees.

5 dimensional Torque at the pitch hip, knees and ankle.

Simplified Full system

9Cognitive Robotics 2010

Simplify system Origin at ankle: -2 DoF. Ignoring the swing leg: -2 DoF. Stance knee straight: -1 DoF Torso at an constant angle: -1 DoF

Total DoF will be 1: a two link invertedpendulum with the upper link at a fixed

angle.10Cognitive Robotics 2010

L = 0,81 mL2 = 0,40 mL1x = 0,4sin(ϕ)L1y = 0,4cos(ϕ)

ϕ = 0,1 radM = 50 kgm = 14 kgI = ml2/3τ = torque

11Cognitive Robotics 2010

V actual velocity Vdes desired velocity (1,0 m/s)

Fx = ground reaction force.

To full state; 3d vector from stance foot to stance hip in sagittal plane.

Proportional-derivative (PD) used. Kp = 1500 Nm; Kd = 150Nm-s; Kp = 1000 Nm; Kd

= 150Nm-s Leg straight and torso at certain angle.

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Shape are similar. Full model at

higher frequency. Difference in

speed and touch in variation touch down model. Torso bobs forward Torque at hip

applied.

13Cognitive Robotics 2010

Swing leg controlled by stance leg.Dynamics and controller are known.

Time and angle at touch down.

Error a few msec.

14Cognitive Robotics 2010

Bending knee (5cm) above ground: inverse kinematics.

Spline at current angle and velocity.

Match velocity swing and stance leg.

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5 DoF 4 Dimensional action space hip and ankle.

Simplified dynamics nearly the same A third state is added; estimated time until touchdown.

Angle of touchdown variable.

Desired velocity of zero Added y2 : legs close to vertical.

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Periods match because of period design parameter.

Impact touchdown counters with rolling torso to vertical.

17Cognitive Robotics 2010

Ankle twist joints are used.Servoing Kp = 500 and Kd = 30 Nm-s

the joints to zero.

Coupling large because shin axis is in line with coronal plane torques.

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Result of pertubation depends on the timing, location and direction of the pertubation.

Unperturbed step: 56 sec.

Front to right not sensible, back to left.

Mid more stable then at the beginning or end.

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Friction affect slipping in forward direction.

Changing the height of the perturbation has a significant effect on perturbing torque around the stance foot: tipping

Changing height +20 has shows the location of the perturbation (right).

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Two ways: Torso lean angle Desired velocity.

Desired velocity 1,0 m/s and lean angle 0,1 rad.

. Simplified system

loses energy from touchdown.

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Change sagital policy forward speed

Estimates of touchdown ankle more accurate.

Changing policies and lean angles in tandem.

First policy 1,0 m/s and second 0,25 m/s. Little energy is los

on short steps at slow speeds.

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The couplings between the subsystems functioning in a full system properly.

Study simulation researchers believe it is well suited in real hardware, because simplified. The control architecture is modular. Also produce other types of walking.

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Future work:Correspond full dynamics to

simplified dynamics Insert torso dynamics for more accurate

touch down model.

Reverse scenario: coronal policy determine the touch down. Provide a good mechanism which policy

was most important to.

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Able to generate policies that are valid for a large region of the high-dimensional state of the full system. Allowing to react on large perturbations.

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Advantages Simplified systems are closely related to the

full systems. Simultaneously adjustment.

Disadvantages: Only simulation is used, perturbations in real

world? No double support phase is used in their

simulation. No torso dynamics in simplified system.

Discussion…26Cognitive Robotics 2010

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