More precise robots: A breakthrough in end-effector accuracy

As robotic technologies are increasingly applied in industrial manufacturing, construction machinery, high-end equipment, and other fields, the demand for motion accuracy continues to grow. Nonetheless, they come with their own set of challenges. In particular, multi-joint serial robots, while offering high flexibility, are prone to the cumulative amplification of small errors at each joint, which ultimately leads to pose errors at the end-effector.

In a new study published in Fundamental Research, a team of researchers from Yanshan University in Qinhuangdao, China, proposed a virtual-constraints-based end-effector pose compensator (VEPC). The method treats the actual angles of specific joints as known inputs and automatically adjusts the remaining joint angles in real time, effectively eliminating the pose errors of the end-effector caused by the joints.

"This is similar to the human arm-small variations at the shoulder, elbow, and wrist can accumulate, resulting in significant changes at the fingertip," explains corresponding author Professor Bin Yu. "Conventional solutions typically address this issue either by improving manufacturing and assembly precision or by performing online compensation using external measurement equipment. However, these methods are expensive and difficult to scale for widespread application."

To achieve precise control of the end-effector pose in serial robots, the new strategy leverages the inverse kinematics adjustment capability inherent to redundant degrees of freedom. "Specifically, the method treats the actual angles of specific joints with errors as "virtual constraints"," shares Yu. "These constraints, together with the desired end-effector pose, are used as the new input to re-solve the inverse kinematics."

Based on the updated solution, the required compensation angles for the remaining joints are determined, effectively counteracting the errors introduced by the constrained joints. As a result, VEPC can automatically eliminates the influence of joint errors on end-effector pose while maintaining the desired pose.

The main novelties of this study are reflected in three aspects:

• Mitigating the influence of joint errors on end-effector pose: Specific joint angles are treated as virtual constraints to replace the secondary constraints. This transforms the inverse kinematics into a problem with a unique solution, which effectively reduces the pose errors of the end-effector caused by the joints.
• Flexible selection of virtual constraints: For serial robots with redundant degrees of freedom, different joints present varying levels of control difficulty. The proposed method allows users to flexibly select appropriate joint angles as virtual constraints, thereby further improving the pose accuracy of the end-effector.
• No additional sensors required: This method can be achieved solely using the position/angle sensors of the joint actuators. This eliminates the need for additional sensing devices and reduces both the software and hardware costs, significantly lowering the barrier to adoption.

Further, the team conducted a series of experiments on a typical planar three-degree-of-freedom serial robot. The results demonstrate that the hip joint exhibits the most significant error amplification effect. When the hip joint is selected as the virtual constraint, by coordinately compensating the angles of the knee and ankle joints, the maximum position error of the end-effector can be reduced by over 75%. Moreover, the method demonstrates high stability under sinusoidal, triangular, and random trajectories, indicating excellent error compensation performance and adaptability to different operating conditions.

"The method can be extended to various types of serial robots. It provides a novel, low-cost, and highly compatible solution for improving the precision at the end-effector," says Yu.

Going forward, the team will further investigate the propagation mechanism between joint errors and end-effector errors. "On this basis, a more versatile VEPC design method will be designed. This achievement is expected to enable broad applications in industrial robots, construction machinery, bionic robots, and other fields," adds Yu.

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Contact the author: Bin Yu, State Key Laboratory of Crane Technology, Yanshan University, Qinhuangdao 066004, China, yb@ysu.edu.cn.

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