The Development of an Adaptive Jacobian Method for Dynamic Constraint Handling in Inverse Kinematics

This paper presents inverse kinematics using a novel adaptive Jacobian method, capable of altering the structure of a device’s Jacobian in response to a variety of dynamic constraints. These constraints are the result of a specific environment, but the adaptive Jacobian method can be applied to any task where the joints of a robot may become periodically inactive. This paper also summarizes the design of a redundant mechanism for payload delivery in a confined space. The redundant arm is capable of folding into a central stack for insertion through a limited access port, and then expanding to deliver the payload. INTRODUCTION The aeronautics industry requires riveting operations inside enclosed sections of aircraft assemblies which are already mostly constructed. Human labor is an unattractive option for this task, as the cramped ergonomic conditions make riveting both inefficient and difficult for the workers. Conventional robots are not an option, as they cannot fit through the limited access ports. Therefore, we are constructing a redundant mechanism that utilizes many degrees of freedom to reach inside of the structure and deliver a tool to key locations. See Figure 1. For this work, the term redundant refers to a mechaFigure 1. TOOL DELIVERY THROUGH LIMITED ACCESS. nism whose configuration space is higher dimension than its effector space. In other words, it has more internal degrees of freedom than are necessary to locate and orient the end effector in space. The same degrees of freedom that benefit the arm’s performance also provide its major challenge: How to coordinate the internal degrees of freedom to move and position an end effector in a useful manner? This problem is often called the inverse-kinematics problem, and gains difficulty as the number of degrees of freedom increases. To address this problem, we analyze the functional relationship between the robot’s configuration space and effector space. In this paper, we define the configuration