IEEE Robotics & Automation Magazine - March 2016 - 36
·
d(d)
·
{j
c
{j
-
R
c
R
I
Current Controller{·
m
1
kv
march 2016
Velocity Controller
kviTv (z + 1)
2(z - 1) Sv
kvp
·
{*m
*
Figure 2. A block diagram of the controller and the plant.
1
L
R
+
kIi Tm(z + 1)
2(z - 1) S i
I
I*
Imax
c*
m
Terrain
Estimator
IEEE ROBOTICS & AUTOMATION MAGAZINE
Gearbox and Joint Friction
·
·
·
xf = sgn({m)c0 + c1{m + c1{3m + x1(fr)
Ka
Tm(z + 1) I
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Motor Electronics
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Locomotion
Controller
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Estimator
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And Dynamics
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Controller
{j*
Joint Torque
Controller
xj*
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Motor Mechanics
Springs
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Actuation (Section IV)
Whole-Body Control
(Section V)
q
Perception
(Section III)
36
c(d)
Spring Mechanics
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a
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a very important role and should
not be ignored for two main reasons. First, the behavior predicted
by simulation becomes much
worse, and, therefore, the learned
model may no longer perform
well on the robot. Second, exploiting the dynamics of the actuators
is crucial to ensuring optimal performance. The key to the success
of our method relies on a model of
the actuator unit that appropriately
trades off accuracy versus computational complexity.
The control method that we
describe in this article is designed
to be applicable for various types
of quadrupedal robots. Nevertheless, we make a few assumptions
regarding actuation and perception capabilitie to generate stable
locomotion skills. The block diagram shown in Figure 2 gives an
overview of our controller and indicates the sections that describe
each building block.
Mechanical Model of the
Quadruped
The controller is primarily tailored
to the mechanical model, as shown
in Figure 3. The rigid multibody
system is composed of 13 bodies,
which are connected through
three-actuated revolute joints per
leg. This mechanical model is described with the generalized coordinates q ! R 15 # SO (3), which
include the pose of the torso with
respect to the world frame and the
joint angles. The generalized velocities u ! R 18 are the linear and angular velocities of the torso and the
joint velocities.
The quadruped model is a
nonsmooth scleronomic dynamical system and can be represented
by a set of equations of the form
M (q) uo - h (q, u) - S < x j J < m = 0, qo = F (q) u,
c i = J i u 6i ! I (q) .
(1)
The mass matrix in (1) is denoted by M. The vector h covers the
nonlinear terms, including Coriolis
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