One-Iteration-per-Update (OIpU) Algorithm Applied to MMPaC (Minimum Motion Planning and Control) of Planar Four-Link Robotic Arm Aided with Zhang Equivalency

In order to efficiently solve the time-varying QP (quadratic programming) problem, some researchers (e.g., Zhang et al) proposed the OIpU-94LVI algorithm. Being the basic idea of the algorithm, let us assume that the time-varying problem may not change significantly in a short period. Therefore, the time-varying QP problem is divided into multiple relatively “static” QP sub-problems using a sampling gap. This paper also investigates a specific MMPaC (minimum motion planning and control) scheme at the joint angular velocity layer based on the kinematic knowledge and Zhang equivalency (ZE), and successfully applies the OIpU-94LVI algorithm to the scheme for the minimum joint motion at the joint angular velocity layer, further confirming the effectiveness of the OIpU-94LVI algorithm in real-world applications. In addition, we use the OIpU-94LVI algorithm to perform computer simulations of real-time MMPaC scheme for the minimal joint motion of a planar redundant robotic arm (i.e., a four-link robotic arm used in this paper for two situations). The experimental tasks involve tracking a bee-shaped path and an epicycloid path. The experimental results are consistent with expectations.