consistent_velocity

A function to compute the consistent velocity of an omnidirectional mobile platform

Omnidirectional platforms can move at different velocities depending on the angular orientation (alpha) of the motion. The consistent velocity is the minimum of the maximum velocities achieved so it is a uniform velocity that the platform can reach in any angular orientation of the motion.

1) Example of computation with a default three-wheeled omnidirectional mobile platform [1]:

[vCons,viMax,vMax] = consistent_velocity(numAlpha,w,wmax)

Where:

- numAlpha is the number of elements in the range of angles of the linear velocity of the platform explored (for example 72).

- w [rad/s] is the angular velocity of the platform to be explored (for example 1 rad/s).

- wmax [rad/s] is the maximum angular velocity of the motors driving the wheels (for example 6.7 rad/s).

- vCons [m/s] is the consistent velocity.

- viMax [m/s] is the vector with the maximum velocity in each direction alpha.

- vMax [m/s] is the maximum value of the maximum velocities in all directions.

2) Example of computation with a custom three-wheeled omnidirectional mobile platform with:

- R [m] is the vector with the distances between the centroids of the robot and each wheel (for example [0.195,0.195,0.195] in [1]).

- r [m] is the vector with the radius of each wheel (for example [0.148,0.148,0.148] in [1]).

- delta [º] is the vector with the angles defining the angular distribution of the wheels (for example [60,180,300] in [1]).

- phi [º] is the vector with the angles defining the angular orientation of the wheels referred to the xwk axis of each wheel when it is perpendicular to the line joining the centroids of the robot and each wheel (for example [0,0,0] in [1]).

- gamma [º] is the vector with the angles of the rollers referred to the ywk axis of each wheel (for example [0,0,0] in [1]).

[vCons,viMax,vMax] = consistent_velocity(numAlpha,w,wmax,R,r,delta,phi,gamma)

The function displays a radial plot showing the maximum velocities and the consistent velocity and the angular velocity of the wheels of the platform required to reach the maximum and the consistent velocity depending on the angular orientation of the motion.