ECE 470: Introduction to Robotics Homework 5
Question 1.
a) Determine the parameters of a 2-segment cubic trajectory where 𝜃0 = 20o
is the initial
point, 𝜃𝑣 = 50o
is the via point and 𝜃𝑔 = 110o
is the goal point. Assume that each segment
spans a duration of 3 seconds and the velocity at the via point is 25 deg/sec. (8 Point)
b) Sketch the graphs for position, velocity and acceleration. (4 Point)
Question 2.
A mobile robot as shown in Figure 1 is considered a differential drive robot that can steer in
direction using the velocity difference between the left and right wheels. The left and right
wheels are driven by controlled motors as shown in Figure 1.
Figure 1 Figure 2
Suppose we plan to move the robot from the initial position to the goal position as shown in
Figure 2. This means that distances from center of rotation to left wheel and right wheel are
1.5r and 0.5r respectively. The ratio of linear velocities of the wheels equals to the ratio of
their distances to the rotation center, i.e 𝑣𝑙
𝑣𝑟
=
𝑟𝑙
𝑟𝑟
, where subscript l and r refer to left and right.
i) What will be the relationship between the angular speeds of the left and right wheels?
(1 Point)
ii) Given that the angular displacement of the right wheel 𝜃𝑟
follows a cubic trajectory from
𝜃0 to 𝜃𝑓, describe angular trajectory of the left motor to maintain the distance r from the
center of rotation. Assume that the coefficients are a0= a1= a2= a3=1. (4 Point)
iii) Describe a control scheme to accomplish this trajectory-following application. (3 Point)
