Dynamics-based forward kinematics estimation for Stewart platform using unscented Kalman filter with extended actuator observations

This paper presents a dynamics-based approach for solving the forward kinematics problem of Stewart–Gough platforms using an Unscented Kalman Filter (UKF) with extended actuator observations. Unlike conventional methods that rely solely on geometric relationships or require additional inertial measurement units, our approach exploits the platform dynamics and utilizes both actuator lengths and their time derivatives as observations. The key insight is that actuator velocity measurements, obtainable from standard encoder hardware through numerical differentiation, provide direct observability of the platform velocity and angular velocity states through the Jacobian relationship, fundamentally resolving the velocity estimation problem inherent in kinematics-only approaches. Through systematic analysis of the platform dynamics, we identify and model a force–angular velocity coupling effect arising from joint damping, which significantly improves the estimation accuracy. We further demonstrate that the direct velocity observability provided by the extended observations enables a simplified angular acceleration model ( ω ˙ ≈ 0 ), which outperforms the full Euler rotational dynamics by avoiding the amplification of force and inertia modeling errors. Comprehensive simulation studies using a high-fidelity Simscape model demonstrate that the proposed method achieves sub-millimeter position accuracy and angular velocity estimation accuracy of 0.004 rad/s, without requiring any additional sensors beyond the standard actuator encoders. Comparative studies against the conventional Newton–Raphson method with numerical differentiation demonstrate that the proposed method achieves comparable position accuracy while providing 14-fold improvement in angular velocity estimation with high-quality velocity measurements, and up to 3-fold improvement in translational velocity estimation under realistic encoder quantization conditions. Parameter sensitivity analysis confirms the robustness of the proposed method across a wide range of filter tuning parameters and measurement noise levels.