Fixed-point computation of robot kinematics in FPGA

Forward and inverse kinematic modeling is essential in trajectory planning for robot manipulators. An approach based on fixed-point format is presented in this paper to accelerate computation. Kinematics of a common industrial robot with last three axes intersecting at a point is first modeled in a form of closed-form solution. A method which integrates look-up tables and angle sum relationships for sine and cosine functions is used to compute trigonometric functions. Also, fourth order series with its coefficients stored in look-up tables is used to calculate inverse trigonometric and square root functions. The presented approach is intended to be applied in FPGA due to its extremely fast computation speed. Its VHDL code is written in ModelSim, which constitutes a simulation block called by SimuLink software. All variables and parameters are represented and calculated in fixed-point format. It shows that the results are almost as accurate as those from a double precision version written in Labview. Acceptable accuracy is still maintained even when robot manipulator is very close to singularities. Further, computation speed is very fast. It takes only 3μs for forward kinematics and 4.5μs for inverse kinematics to complete the computation.