Lagrangian Based Mathematical Modeling and Experimental Validation of a Planar Stabilized Platform for Mobile Systems

Typical operating conditions for mobile sensor systems, and in particular mobile robots, exhibit a wide range of mechanical disturbances due their ego-motion. Sensor systems mounted on these mobile platforms often suffer to varying degrees from these disturbances. The quality of acquired data is degraded as a result. For instance, the quality of captured video frames from an onboard camera greatly depends on the angular velocity of the body on which the camera is mounted. Motion blur degradation results if large angular motions are present. In order to compensate for such disturbances, stabilization platforms are used. A common approach is measuring body movements using inertial sensors and attempting their cancellation with actuators and control systems. Design of high performance control systems often requires analytical system models. In this article, a planar stabilization platform is considered, to develop and study its kinematic and simple-to-complex dynamic model. The mathematical derivation of the model is presented with and without neglect of the actuator mass components as well as friction effects. This is followed by the comparative validation of these model alternatives against a realistic numerical model fitted to physical experimental data. The results demonstrate that the analytical model, in particular with the actuator mass and friction components included, provides a high degree of fit to the actual behavior.