Globally exponentially stable observer for vision-based range estimation

A reduced-order nonlinear observer is developed to estimate the distance from a moving camera to a feature point on a static object (i.e., range identification), where full velocity and linear acceleration feedback of the calibrated camera is provided. The contribution of this work is to develop a global exponential range observer which can be used for a larger set of camera motions than existing observers. The observer is shown to be robust against external disturbances in the sense that the observer is Lp∀p∈[1,∞]Lp∀p∈[1,∞] stable even if the target object is moving or the camera motion is perturbed. The presented observer identifies the range provided an observability condition commonly used in literature is satisfied and is shown to be exponentially stable even if camera motion satisfies a less restrictive observability condition. A sufficient condition on the observer gain is derived to prove stability using a Lyapunov-based analysis. Experimental results are provided to show robust performance of the observer using an autonomous underwater vehicle (AUV).