Estimation of object kinematics from point data

One of the fundamental problems arising in kinematics is that of determining object position, velocity and acceleration from given point position, velocity and acceleration data. This type of problem is frequently encountered in robotics, biomechanics, real-time control of space structures, automatic guided vehicles, etc. Complications arise when redundant data are used and when the data have errors. Chutakanonta and Gupta proposed two simple and elegant methods for the estimation of object position from the given point position data. The present work is an extension of these methods for estimating the object velocity and acceleration states from the given point position, velocity and acceleration data. The method proposed herein uses Singular Value Decomposition (SVD) to effectively estimate the object velocity and acceleration states. Such matrix decompositions can be performed by using readily available matrix-oriented software like MATLAB and can be successfully used to simplify the solution of the over-determined system of equations encountered in these types of problems. Several hypothetical examples and examples that simulate practical situations are presented to determine the effectiveness, robustness and applicability of the proposed method. The method is found to be very effective in estimating the object velocity and acceleration states in the presence of imprecise and redundant data as well as for nearly co-planar point data.