Trajectory Formulation
Mathematical motion profiles define the velocity and acceleration curves of high-speed industrial robotics. Using a fifth-order polynomial for path planning produces a continuous transition in position, velocity, and acceleration by solving a system of equations with six boundary conditions. These conditions specify the start and end values for position, speed, and acceleration.
This approach generates a mathematical curve that prevents sudden movements at the start and finish of a travel path.
Motion Smoothing
Mechanical wear decreases when the acceleration curve of a pick-and-place gantry is smooth and continuous. By applying a fifth-order polynomial to the trajectory, the control system ensures that the first derivative of acceleration, which represents jerk, remains finite and continuous throughout the entire move. This continuous derivative eliminates the sharp shocks associated with simpler trapezoidal velocity profiles.
It extends the operating life of linear motors and ball screws, reducing maintenance costs while allowing the machine to operate at higher cycle frequencies without losing structural rigidity.
Controller Execution
Real-time processors calculate these trajectory curves to drive the motor amplifiers. Because the fifth-order polynomial requires substantial calculation, DSP chips must run these algorithms at high update rates to adjust motor currents. This processing results in precise positioning.
