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In this work the authors present a novel algorithm for estimating the odometry of "C" legged robots with compliant legs and an analysis to estimate the pose of the robot. Robots with "C" legs are an alternative to wheeled and tracked robots for overcoming obstacles that can be found in different scenarios like stairs, debris, etc. Therefore, this kind of robot has become very popular for its locomotion capabilities, but at this point these robots do not have developed algorithms to implement autonomous navigation. With that objective in mind, the authors present a novel algorithm using the encoders of the legs to improve the estimation of the robot localization together with other sensors. Odometry is necessary for using some algorithms like the Extended Kalman Filter, which is used for some autonomous navigation algorithms. Due to the flexible properties of the "C" legs and the localization of the rotational axis, obtaining the displacement at every step is not as trivial as in a wheeled robot; to solve those complexities, the algorithm presented in this work makes a linear approximation of the leg compressed instead of calculating in each iteration the mechanics of the leg using finite element analysis, so the calculus level is reduced. Furthermore, the algorithm was tested in simulations and with a real robot. The results obtained in the tests are promising and together with the algorithm and fusion sensor can be used to endow the robots with autonomous navigation. [ABSTRACT FROM AUTHOR]