IEEE Robotics & Automation Magazine - December 2022 - 95

Side ViewTop View
Joint
70 mm
54 mm
100 mm
100 mm
Housing
PCB Board
Gears and Servo
Lateral
Rotation
Forward
Rotation
Angular Sensor
Passive Wheels
Figure 1. The snake-like robot and its module dimensions. PCB: printed circuit board.
narrowing the gap between the simulation and the real world.
There are several key parameters that directly determine the
accuracy of the dynamic model, such as the mass of the robot,
inertia, friction, and other physical parameters.
Modeling Mass
The mass can be weighted exactly by measuring the module
of the prototype, while the moment of inertia is estimated
from its CAD assembly, in which each component is
given its material.
Modeling Actuation
The simulated servo system consists of a position-controlled
motor, feedback signal of the joint position, and gear ratio.
For the sake of simplicity, by setting the gear ratio to one, we
directly map the motor position to the output position of the
servo system. The torque is limited to a range of [. ,. ]46 46in
the Newton meter based on specifications of the servo.
Modeling Friction
To imitate this anisotropic friction property, each robot module
is equipped with two passive wheels. Those passive wheels
enable a minimum friction in the direction of rotation and a
high friction in the lateral direction (see Figure 1). To obtain
realistic movements, we directly measured the friction coefficients
for these two directions in the real world.
Energy-Efficiency Metric
We aim to design gaits that can make snake-like robots move
energy efficiently and in the meantime keep a steady speed of
the movement. In this work, we define the power efficiency
metric to evaluate the performance of all gaits.
Table 1. Technical details of the robot module.
Parameters
Dimensions
Quantity
Width: 70 mm; length: 100 mm;
height: 54 mm
Mass
Servo
Gearbox
Communication
Sensors
Power
Control rate
Body: 202 g; one wheel: 2.2 g
Max torque: 12.8 kg·cm; max
speed: 0.07 s/60°
Gear ratio: 151:43
CAN bus
AS5047D (resolution: 0.022°)
Voltage: 24 V; max current: 10 A
20 Hz
Max: maximum; CAN: controller area network.
P = R xz where izo
o
i =1 ii
The total power P of the robot can be calculated by adding
N
up the power of all the N joints, which can be calculated as
,
x j is the product of its applied force fi
parameter hi
actuators with a limited force of fmax
is calculated as
P = 1 / maxmax
ii i
t
N fh
fh
N
i =1
i
o
o
z
z
is the velocity of joint i. The torque
and its gear constant
(the length of the actuator). The model uses
as the maximum force
in both directions. With this property, the normalized power
consumption Pt
.
This normalized power consumption Pt will be further used
for reward definition.
With the power P and the velocity v, several efficiency
metrics can be calculated. The usual way is to calculate the
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
95
IEEE Robotics & Automation Magazine - December 2022

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