Trajectory Planning

Each of the five fingertips must follow a set path through 3D space to rotate the platform. The paths consist of two trajectories:

1. Fingertip is in contact with the platform
2. Fingertip is not in contact with the platform

Four out of the five fingertips will always be in contact with the platform (state 1) while the remaining fingertip will be in the return state and not in contact with the platform (state 2).

State 1: Circular Path

A circle is generated with a given number of data points and a specified diameter. The circle is split into five sections so that each fingertip covers a portion of the platform.

State 2: Parabolic Z Path

When a fingertip releases from the platform, it reverses the circular path it made previously; however, it also dips below the z height of the other fingertips. This z element follows the simple form of y=ax^2 + b where the a and b coefficients determine the depth and concavity the fingertip should follow.

Trajectory Visuals

Combining the two trajectories for one of the fingers yields the results below where the blue and orange lines represent states 1 and 2, respectively.

Combining all five fingers yields the trajectories below. In reality, some of the endpoints between fingers are removed to prevent collisions when two adjacent fingers are switching states. Additionally, offsets can be adjusted for each finger to account for manufacturing and assembly tolerances.

With the developed trajectories, the kinematics can be generated.