### Abstract:

This thesis presents a control system for a walking
machine leg. The leg is representative of one of the six
legs required for a proposed walking machine based on the
geometry of the darkling beetle.
Each of the three joints is controlled by a DC servo
motor mounted to the base of the leg. The speed of the
motors is controlled with pulse width modulation. Feedback
of joint positions is accomplished with potentiometers
mounted on the actual joints.
A five-point path, forming a rectangle in the global
coordinate system, is used as a skeleton of the path of
movement. Desired times and accelerations from point to
point are used to develop the path of movement, which
smoothes corners and velocity transitions along the path.
To create a model of the dynamics of each joint, a
constant motor speed is output and the joint velocity and
joint angle are recorded. From several trials at several
different motor speeds, relationships between the joint
velocity, joint angle, and motor speed can be found. This
data is then least squares fit in two dimensions to give two
second order functions. The first function uses the desired
joint angle to calculate the variance from the mean joint
velocity. This variance is then added to the desired joint
velocity and is used in the second function to calculate the
needed motor signal.
Feedback control is accomplished using a PID control
system. Because of the high level of noise in the feedback
signal, a digital noise filter is used. Both moving average
and linear regression techniques are examined.
Performance of the system is measured by comparing the
actual path in Cartesian coordinates to the desired path of
movement. The RMS error is taken along the path, during the
time frame of the ideal system. The maximum Cartesian error
along the path is also used in evaluation.
To determine suitable feedback gain combinations,
several experiments are run and evaluated. Data is plotted
and suitable values are chosen for the feedback gains based
on their performance and sensitivity to change in
performance.
The performance of the leg is measured for a basic
rectangular path, the basic path with a variation in step
angle, and the basic path with a constant body velocity.