Efficient FPGA hardware implementation for robot manipulator kinematic modeling using rational trigonometry

A common approach to model kinematics for robot manipulators uses functions such as sin(), cos() and atan(),however, the rational trigonometry allows to exclude the use of these transcendental functions. Most of the computing processing to control a manipulator is dedicated to solving its kinematics, therefore, reduce the complexity of kinematic equations leads to a more compact and efficient model. In this paper, we propose a geometric analysis to solve the kinematics of robot manipulator of up to three degrees of freedom, avoiding the use of transcendental functions in the kinematic equations. We present three kinematic models for the mechanism positions and theirimplementations in an FPGA. The experimental results show that our proposed models: 1) use less logic elements compared with an implementation based on parallel CORDIC and 2) has lower latency respect with iterative CORDIC implementation.