Assume the following scenario, with two horizontal planes and a stair, where and the inclination of the stair .
The agent has a desired speed on the horizontal plane and a different desired speed on the stair .
Given a stair connecting two hirozontal floors, we define the following functions:
Function of the desired speed
Taking the previously introduced quantities into consideration, we can define the desired speed od the agent with respect to its component as
is a constant.
The following figure shows the changes of the desired speed with repsect to the inclination of the stair . The steepter the inclination of the stair, the faster is the change of the desired speed.