Uncertainty and Sensitivity Analysis

Uncertainty in engineering systems comes from various sources such as manufacturing imprecision, assembly errors, model variation, and stochastic operating conditions. It is important to derive the mathematical model for the spatial measurement uncertainty and the sensitivity analysis of the robot’s kinematic parameters for a sensor-fused robotic system. Studies on uncertainty analysis were done using probabilistic models without emphasising the context of multiple sensor mounted on the robot. And mostly, the local sensitivity analysis is studied to estimate the variation of input parameters on the output using the Jacobian. This chapter presents the propagation relationship of the uncertainties in the camera’s image space, the 2D space of the laser scanner, the Cartesian space in the world coordinate, and the tool space. Since a vision sensor is a vital sensor for localization, it is essential to have performance maps. Here, we perform an analytical and quantitative simulation to model uncertainty in the pose from camera and depth sensors that are mounted on a KUKA KR5 Arc robot’s end-effector. A quantitative analysis of the spatial measurement of the sensor-fused system is performed by utilizing the covariance matrix in the depth image space and the calibrated sensor parameters using the proposed mathematical model. Moreover, sensitivity analysis assesses the contributions of the inputs to the uncertainty.