Sensor Observability Index: Evaluating Sensor Alignment for Task-Space Observability in Robotic Manipulators

In this paper, we propose a preliminary definition and analysis of the novel concepts of sensor observability, sensor manipulability, and their respective indices. The goal is to analyse and evaluate the performance of distributed directional or axial-based sensors to observe specific axes in task space as a function of joint configuration in serial robot manipulators. For example, joint torque sensors are often used in serial robot manipulators and assumed to be perfectly capable of estimating end effector forces, but certain joint configurations may cause one or more task-space axes to be unobservable as a result of how the joint torque sensors are aligned. The proposed sensor observability provides a method to analyse the quality of the current robot configuration to observe the task space. Sensor manipulability, on the other hand, measures the robot's ability to increase or decrease that observational quality, analogous to end effector positional manoeuvrability as measured by the traditional kinematic manipulability. Parallels are drawn between sensor observability and the traditional kinematic Jacobian for the particular case of joint torque sensors in serial robot manipulators. Although similar information can be retrieved from kinematic analysis of the Jacobian transpose in serial manipulators, sensor observability is shown to be more generalizable in terms of analysing non-joint-mounted sensors and other sensor types. In addition, null-space analysis of the Jacobian transpose is susceptible to false observability singularities. Simulations and experiments using the robot Baxter demonstrate the importance of maintaining proper sensor observability in physical interactions.