The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which remained open for a long time. We give a solution to the problem in this paper assuming that only the bearing of a feature point, and biased linear acceleration and rotational velocity of a robot -- all in the body-fixed frame -- are available. Further, in contrast to existing related results, we do not need the value of the gravitational constant either. The proposed approach builds upon the parameter estimation-based observer recently developed in (Ortega et al., Syst. Control. Lett., vol.85, 2015) and its extension to matrix Lie groups in our previous work. Conditions on the robot trajectory under which the observer converges are given, and these are strictly weaker than the standard persistency of excitation and uniform complete observability conditions. Finally, we apply the proposed design to the visual inertial navigation problem. Simulation results are also presented to illustrate our observer design.
翻译:设计一个全球趋同位置观察者,以观察视觉信息的地貌点,这是一个具有挑战性的问题,特别是对于仅进行惯性测量和不假定统一可观察性的情况来说,这种假设长期开放。我们在本文件中提出一个问题的解决办法,假定只有带有地貌点和偏向线性加速和旋转速度的机器人 -- -- 全部在机身固定框架中 -- -- 才能使用。此外,与现有的相关结果相比,我们也不需要引力常数的价值。提议的方法以最近(Ortega et al., Syst. Control. Lett., vol.85, 2015)开发的基于参数估计的观察员为基础,并扩大到我们以前工作中的基数 " 利 " 组。观察者聚集的机器人轨迹条件严格地弱于标准的持续引力和统一完整易观察性条件。最后,我们对视觉惯性导航问题适用拟议的设计。模拟结果还用来说明我们观察者的设计。