This paper introduces the Visual Inverse Kinematics problem (VIK) to fill the gap between robot Inverse Kinematics (IK) and visual servo control. Different from the IK problem, the VIK problem seeks to find robot configurations subject to vision-based constraints, in addition to kinematic constraints. In this work, we develop a formulation of the VIK problem with a Field of View (FoV) constraint, enforcing the visibility of an object from a camera on the robot. Our proposed solution is based on the idea of adding a virtual kinematic chain connecting the physical robot and the object; the FoV constraint is then equivalent to a joint angle kinematic constraint. Along the way, we introduce multiple vision-based cost functions to fulfill different objectives. We solve this formulation of the VIK problem using a method that involves a semidefinite program (SDP) constraint followed by a rank minimization algorithm. The performance of this method for solving the VIK problem is validated through simulations.

翻译：本文提出了视觉逆运动学问题，旨在填补机器人逆运动学与视觉伺服控制之间的研究空白。与传统逆运动学问题不同，视觉逆运动学问题在满足运动学约束的同时，还需满足基于视觉的约束条件。本研究针对包含视场约束的视觉逆运动学问题建立了数学模型，该约束要求机器人搭载的摄像头必须持续观测到目标物体。我们提出的解决方案基于引入虚拟运动链的概念，该运动链连接物理机器人与目标物体，从而使视场约束等价于关节角度的运动学约束。在此过程中，我们引入了多种基于视觉的代价函数以实现不同的优化目标。通过结合半定规划约束与秩最小化算法的方法，我们对视觉逆运动学问题的数学模型进行求解。仿真实验验证了该方法在解决视觉逆运动学问题上的性能表现。