The Kalman filter gain can be extracted from output signals but the covariance of the state error cannot be evaluated without knowledge of the covariance of the process and measurement noise Q and R. Among the methods that have been developed to estimate Q and R from measurements the two that have received most attention are based on linear relations between these matrices and: 1) the covariance function of the innovations from any stable filter or 2) the covariance function of the output measurements. This paper reviews the two approaches and offers some observations regarding how the initial estimate of the gain in the innovations approach may affect accuracy.
Serial robot manipulators have their servo motors with reduction gears on the link joints. When it comes to hyper-redundant robots, this kind of joint actuation mechanism cannot be implemented since this makes hyper-redundant robots too heavy. Instead, cable driven mechanisms are preferred. However, the positioning accuracy is negatively affected by the cables. This paper addresses the positioning accuracy problem of cable driven hyper-redundant robots by employing a 2-DOF robotic arm whose modules are counter-balanced. While the actuators connected to the base actively do most of the work using cables and springs, light and compact actuators connected to the links produce precise motion. The method will result in compact, light and precise hyper-redundant robotic arms. The above-mentioned procedure governed by a control software including a 2D simulator developed is experimentally proved to be a feasible method to compensate the gravitational torque successfully.
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