Development of Parallel Delta Robot System Controller Based on Raspberry Pi and FPGA

Abstract

This paper presents a system control design on 2 axes “Delta Industrial Robot”. The control system utilizes both the embedded technology and the “Raspberry Pi" which is a low power consumption PC with open source operating system. The user can communicate with the PC and FPGA (Field Programmable Gate Array) via the system GUI interface. The FPGA acts as dedicated hardware to provide both the efficiency and flexibility for the closed-loop servo control system.To calculate all related kinematics equations for the robot, look up table approach has been implemented to reduce the calculation complexity. Python programs are also implemented to create and search the look up tables. The inverse kinematics is the key to find the position of the robot. A test load of 0.2 kg at the velocity of 2.618 m/s, the S.D. of the end effector’s position of the test result is within 0.06 mm.

Controller Design for a Delta Robot Using Lagrangian Multipliers

“…6, for subsequent dynamics computations. Figure 6 shows the redesigned system dynamics with the Lagrangian multipliers employed to satisfy the constraints in equation (11). The augmented controller successfully achieves the movable platform's commanded motions while tracking a given 3D circular trajectory and avoiding singularities within a limited workspace range.…”

“…Delta robot applications also demand compact mechanisms with lightweight controllers for the industry 10 , and embedded electronics using wireless interfacing become mandatory. Some researchers utilized an FPGA (Field Programmable Gate Array) device as dedicated hardware to provide a closed-loop servo control system, which exercises a Delta robot's kinematics equations to perform fast and accurate positioning 11 . In addition, other researchers designed two controllers to ensure stability and performance of a Delta robot closed-loop system, and that study embedded the control algorithms into a myRIO hardware device through the LabVIEW deployments 12 .…”

“…results in 𝑛 equations of motions in the following general form: 𝐌(𝒒)𝒒̈+ 𝐂(𝒒, 𝒒̇) + 𝐆(𝒒) + 𝐉 𝑻 (𝒒)𝝀 = 𝐐 (11). where 𝝀 is a vector consisting of the Lagrangian multipliers.For deriving the Lagrangian multipliers, rewrite the above equation as: 2 ∑ 𝜆 𝑖 (𝑝 𝑥 + 𝑒 𝑐𝑜𝑠 𝜑 𝑖 − 𝑓 𝑐𝑜𝑠 𝜑 𝑖 − 𝑟 𝑓 𝑐𝑜𝑠 𝜑 𝑖 𝑐𝑜𝑠 𝜃 𝑖 ) = (𝑚 𝑝 + 3𝑚 𝑏 )𝑝̈𝑥…”