Solution of the Direct Position Kinematics Problem of the General Stewart Platform Using Advanced Polynomial Continuation

Abstract In this paper the direct position kinematics problem of the most general geometry of the Stewart platform has been solved numerically. It is found that this problem has exactly 40 distinct, finite solutions. No closed form solutions are available for this problem. This problem was addressed for the first time by Raghavan recently, and the results obtained here are in agreement with the ones obtained by Raghavan. The formulation and the variable set used in this work lead to a simpler polynomial system of lower overall degree. Further, the geometric parameters of the general Stewart platform have been used to generate a ‘near-general’ Stewart platform. Even though the near-general Stewart platform also has exactly 40 finite, distinct, configurations, it is represented by much simpler polynomial equations. The polynomial system obtained from this near-general Stewart platform is used as the start system in an advanced polynomial continuation scheme to solve the general Stewart problem. This process eliminates a large number of solutions at infinity that have no geometric significance. This leads to an efficient numerical algorithm that is about twenty times faster than traditional continuation schemes.