Page 201 - Introduction to Autonomous Mobile Robots

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• Unequal floor contact (slipping, nonplanar surface, etc.). Chapter 5
Some of the errors might be deterministic (systematic), thus they can be eliminated by
proper calibration of the system. However, there are still a number of nondeterministic
(random) errors which remain, leading to uncertainties in position estimation over time.
From a geometric point of view one can classify the errors into three types:
1. Range error: integrated path length (distance) of the robot’s movement
→ sum of the wheel movements
2. Turn error: similar to range error, but for turns
→ difference of the wheel motions
3. Drift error: difference in the error of the wheels leads to an error in the robot’s angular
orientation

Over long periods of time, turn and drift errors far outweigh range errors, since their con-
tribution to the overall position error is nonlinear. Consider a robot whose position is ini-
x
tially perfectly well-known, moving forward in a straight line along the -axis. The error
d
y
in the -position introduced by a move of meters will have a component of dsin ∆θ ,
which can be quite large as the angular error ∆θ grows. Over time, as a mobile robot moves
about the environment, the rotational error between its internal reference frame and its orig-
inal reference frame grows quickly. As the robot moves away from the origin of these ref-
erence frames, the resulting linear error in position grows quite large. It is instructive to
establish an error model for odometric accuracy and see how the errors propagate over
time.

5.2.4 An error model for odometric position estimation
Generally the pose (position) of a robot is represented by the vector

x
p = y (5.1)
θ

For a differential-drive robot the position can be estimated starting from a known posi-
tion by integrating the movement (summing the incremental travel distances). For a dis-
crete system with a fixed sampling interval ∆t the incremental travel distances
( ∆x ∆y ∆θ;; ) are

⁄
∆x = ∆scos ( θ + ∆θ 2) (5.2)