IEEE Robotics & Automation Magazine - September 2018 - 29

(b)

(c)

Controller Behaviors
(3-D, Free Standing)

t

(c)

Energy Injection

Controller
Blending

Parameterized LegLengthExtension
Trajectory

Stride Trajectory

VirtualToeTrajectory

+ TouchdownTarget
+

Torso Balance

LegAngleTorque

Interp(a,b,t)

FF(v)

P(v,kp)

P(v,kp)

+
-

(a)

FL(e,kp,kd)

legForce

(a)
µ

1

PD(e)

Pitch Error

Balancing Torque

ory

raject

Toe T

motorTorqueB

motorTorqueA

Normal Force

september 2018

*

PD(v)

(a)

v

Shear Limit

1
k
v

(b)

Horizontal
Velocity

Balancing Force

e
T

Touchdown Target

M
Co

ry

cto

je
ra

Virtual Toe

Figure 6. A high-level view of the three main behaviors of the control algorithm. (a) Torso balance attempts to keep the torso upright, applying restoring torques at the hip based on a
feedback-linearization control law. Because each leg has both stance and aerial phases, the balance controller must be blended in and out as the contact force changes. The resulting
shear force on the ground is always limited to be within an approximate friction cone. (b) Each stride trajectory has a target touchdown location for the toe, where the toe will be groundspeed matched and lowered toward the ground. This vertical descent continues even after the physical toe begins contact and the virtual toe is driven deeper into the ground, where
the leg compliance can supply restoring forces. Vertical descent also improves the chances that a disturbance will affect the height of the contact only. The touchdown target location is a
result of feed-forward processing of the current velocity adjusted by the difference between the current and target velocities. (c) Energy injection is parameterized as extra leg extension in
the second half of the stance phase. Stepping and energy injection are both driven by an internal clock cyclically progressing through the phase [0,1].

F

clock

targetVelocity

clock

lastTouchdown

targetVelocity

currentVelocity

bodyAngleError

Walking/Running Controller
(One Per Leg, Out of Phase)

Compliance

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

29

IEEE Robotics & Automation Magazine - September 2018

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2018

Contents
IEEE Robotics & Automation Magazine - September 2018 - Cover1
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IEEE Robotics & Automation Magazine - September 2018 - Contents
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IEEE Robotics & Automation Magazine - September 2018 - Cover3
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