Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection and in-vitro fertilization. Robotic cell injection systems provide the automation of the process as opposed to the manual and semi-automated cell injection systems, which require expert operators and involve time consuming processes and also have lower success rates. The automation of the cell injection process is obtained by controlling the orientation and movement of its various components, like injection manipulator, microscope etc., and planning the motion of the injection pipette by controlling the force of the injection. The conventional techniques to analyze the cell injection process include paper-and-pencil proof and computer simulation methods. However, both these techniques suffer from their inherent limitations, such as, proneness to human error for the former and the approximation of the mathematical expressions involved in the numerical algorithms for the latter. Formal methods have the capability to overcome these limitations and can provide an accurate analysis of these cell injection systems. Model checking, i.e., a state-based formal method, has been recently used for analyzing these systems. However, it involves the discretization of the differential equations capturing the continuous dynamics of the system and thus compromises on the completeness of the analysis of these safety-critical systems. In this paper, we propose a higher-order-logic theorem proving (a deductive-reasoning based formal method) based framework for analyzing the dynamical behavior of the robotic cell injection systems upto 4-DOF. The proposed analysis, based on the HOL Light theorem prover, enabled us to identify some discrepancies in the simulation and model checking based analysis of the same robotic cell injection system.

中文翻译：

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使用 HOL Light 对高达 4 自由度的机器人细胞注射系统进行正式验证

细胞注射是将小样本物质输送到生物细胞中的一种方法，广泛用于药物开发、基因注射、胞浆内精子注射和体外受精。与手动和半自动细胞注射系统相比，机器人细胞注射系统提供了过程的自动化，后者需要专家操作员并涉及耗时的过程，并且成功率也较低。细胞注射过程的自动化是通过控制其各个部件的方向和运动来实现的，如注射机械手、显微镜等，并通过控制注射力来规划注射吸管的运动。分析细胞注射过程的常规技术包括纸笔证明和计算机模拟方法。然而，这两种技术都有其固有的局限性，例如，前者容易出现人为错误，后者的数值算法中涉及的数学表达式近似。正式的方法有能力克服这些限制，并可以提供对这些细胞注射系统的准确分析。模型检查，即基于状态的形式化方法，最近已被用于分析这些系统。然而，它涉及捕获系统连续动态的微分方程的离散化，因此会损害这些安全关键系统分析的完整性。在本文中，我们提出了一种基于高阶逻辑定理证明（一种基于演绎推理的形式方法）的框架，用于分析机器人细胞注射系统高达 4 自由度的动力学行为。所提出的分析基于 HOL Light 定理证明器，使我们能够识别基于相同机器人细胞注射系统的模拟和模型检查分析中的一些差异。