Estimation of general three-dimensional motion of an unknown rigid body under no external forces and moments

Abstract

This paper presents a method, which is applicable to autonomous space robotic missions, to estimate and to predict the general three-dimensional motion of an unknown rigid body under no external forces and moments using visual information. The authors assume that both geometric and inertial parameters of the rigid body are completely unknown to consider a general situation. Thus it is difficult to identify the absolute orientation of an object due to lack of knowledge. However, it is possible to estimate the angular velocity from two successive images. Therefore the problem is how to get the description of orientation as a function of time from a sequence of angular velocities based on Euler's equation of motion. Although the solution of Euler's equation is complicated and expressed with the elliptic functions, it can be also interpreted geometrically with Poinsot's ellipsoid, which is useful to understand this problem. The solution is classified into four cases: asymmetric, non-periodic, axially symmetric and single axial. Four parameters of dynamics and a reference frame are essential to describe the motion. Since the solution is expressed in terms of the body frame, it cannot be directly used for the estimation of the parameters from the angular velocity vector in terms of the camera frame. To avoid this problem, focusing on the magnitude of angular velocity and the herpolhode, four models corresponding to the four cases are employed. Moreover, an integrated strategy to make proper use of these models is proposed. The effectiveness and limitation of this method are discussed, through computer simulations for various kinds of motion.