A comparative analysis of initial-pose self-calibration algorithms for underactuated cable-driven parallel robots

Abstract Underactuated Cable-Driven Parallel Robots ( UACDPRs ) typically rely on relative internal sensors to estimate the end-effector ( EE ) state. Therefore, at startup, the reference values of the quantities measured by these sensors are unknown, and so is the initial pose of the EE . The problem of determining the reference values of the internal sensors is called initial-pose self-calibration. The latter is often formulated as an overdetermined system of nonlinear equations and solved using nonlinear weighted least-squares methods, minimizing the error between modeled and measured variables, and its effectiveness is highly influenced by the choice of measurement configurations, as well as the motion planning and control strategy used to reach them. This work presents two practical data acquisition methods for initial-pose self-calibration of UACDPRs , aiming to reduce the overall time required by the procedure and enhance process automation. The first method is slower but richer in data, as it relies on equilibrium poses and, therefore, can leverage cable-tension data, whereas the second method is faster and is based on geometric constraints only. The performance of the methods is evaluated in terms of acquisition time, number of measurements, and calibration accuracy on a 4-cable UACDPR prototype. The results highlight the merits and shortcomings of both methods, namely, trade-offs between the velocity of data collection and the precision of pose estimation.