Probabilistic approaches to the $$ AXB = YCZ $$ calibration problem in multi-robot systems

Simultaneous Calibration of the Hand-Eye, Flange-Tool and Robot-Robot Relationship in Dual-Robot Collaboration Systems

A multi-robot collaboration system can complete more complex tasks than a single robot system. Ensuring the calibration accuracy between robots in the system is a prerequisite for the effective inter-robot cooperation. This paper presents a dual-robot system for orthopedic surgeries, where the relationships between hand-eye, flange-tool, and robot-robot need to be calibrated. This calibration problem can be summarized to the solution of the matrix equation of AXB=YCZ. A combined solution is proposed to solve the unknown parameters in the equation of AXB=YCZ, which consists of the dual quaternion closed-form method and the iterative method based on Levenberg-Marquardt (LM) algorithm. The closed-form method is used to quickly obtain the initial value for the iterative method so as to increase the convergence speed and calibration accuracy of the iterative method. Simulation and experimental analyses are carried out to verify the accuracy and effectiveness of the proposed method.

Physician-Friendly Tool Center Point Calibration Method for Robot-Assisted Puncture Surgery

After each robot end tool replacement, tool center point (TCP) calibration must be performed to achieve precise control of the end tool. This process is also essential for robot-assisted puncture surgery. The purpose of this article is to solve the problems of poor accuracy stability and strong operational dependence in traditional TCP calibration methods and to propose a TCP calibration method that is more suitable for a physician. This paper designs a special binocular vision system and proposes a vision-based TCP calibration algorithm that simultaneously identifies tool center point position (TCPP) and tool center point frame (TCPF). An accuracy test experiment proves that the designed special binocular system has a positioning accuracy of ±0.05 mm. Experimental research shows that the magnitude of the robot configuration set is a key factor affecting the accuracy of TCPP. Accuracy of TCPF is not sensitive to the robot configuration set. Comparison experiments show that the proposed TCP calibration method reduces the time consumption by 82%, improves the accuracy of TCPP by 65% and improves the accuracy of TCPF by 52% compared to the traditional method. Therefore, the method proposed in this article has higher accuracy, better stability, less time consumption and less dependence on the operations than traditional methods, which has a positive effect on the clinical application of high-precision robot-assisted puncture surgery.

Quantizing Euclidean Motions via Double-Coset Decomposition

Concepts from mathematical crystallography and group theory are used here to quantize the group of rigid-body motions, resulting in a "motion alphabet" with which robot motion primitives are expressed. From these primitives it is possible to develop a dictionary of physical actions. Equipped with an alphabet of the sort developed here, intelligent actions of robots in the world can be approximated with finite sequences of characters, thereby forming the foundation of a language in which robot motion is articulated. In particular, we use the discrete handedness-preserving symmetries of macromolecular crystals (known in mathematical crystallography as Sohncke space groups) to form a coarse discretization of the space SE(3) of rigid-body motions. This discretization is made finer by subdividing using the concept of double-coset decomposition. More specifically, a very efficient, equivolumetric quantization of spatial motion can be defined using the group-theoretic concept of a double-coset decomposition of the form Γ\SE(3)/Δ, where Γ is a Sohncke space group and Δ is a finite group of rotational symmetries such as those of the icosahedron. The resulting discrete alphabet is based on a very uniform sampling of SE(3) and is a tool for describing the continuous trajectories of robots and humans. An efficient coarse-to-fine search algorithm is presented to round off any motion sampled from the continuous group of motions to the nearest element of our alphabet. It is shown that our alphabet and this efficient rounding algorithm can be used as a geometric data structure to accelerate the performance of other sampling schemes designed for desirable dispersion or discrepancy properties. Moreover, the general "signals to symbols" problem in artificial intelligence is cast in this framework for robots moving continuously in the world.