# State Estimation of Over-Sensored Systems Applied to a Low-Cost Robotic Manipulator
## 1 Introduction  
Robotics has been an integral part of society for several decades. It is present in industry, the medical field, and the military, among others. Wherever physical labor is required, robotics serves as a more economical, stronger, more precise, and overall more effective alternative to human labor. In addition, robots have been proven to be capable of performing tasks that are otherwise dangerous, if not impossible, for people to do, such as search and rescue missions in dangerous environments. Within this very broad field, one of the most explored areas is the control of rigid structure robotic manipulators. There are still numerous problems to be solved within this scope, like the manipulator's configuration (number and type of joints, link's shape and size), that must be chosen according to its objective; its motors must be precisely controlled, and information such as the pose of the manipulator must be known to serve as an input to the controller. This last problem is commonly called in the literature state estimation. Being a common problem, many algorithms have been developed to help solve it. These algorithms read information from imperfect sensors and merge it to find what is believed to be the best estimate of the system's state. In the context of robotic manipulators, there already are numerous examples of the usage of estimators to determine their pose. In most cases, the pose is simply defined as the angles of each joint, and it is estimated using non-linear variants of the Kalman filter. For example, in [1], several instances of the extended Kalman filter were chained to estimate the angles and angular velocities of each joint. In this example, the models of the manipulator are defined according to the orientation of the axes of rotation of the joints and the placement of the inertial measurement units, and the base is assumed fixed. In [2], the authors proposed to estimate the same variables using the extended Kalman filter by modeling them as a function of the inertial sensors' measurements. Despite being a moregeneric approach, it requires each link of the manipulator to be equipped with one triad of gyroscopes and two triads of accelerometers. The study in [3] focused on the description of a variant of the Kalman filter named the adaptive square-root unscented Kalman filter and applied it to this context. It compares the results of this filter with the extended Kalman filter, the unscented Kalman filter, and its adaptive counterparts. It demonstrates that these variants are mostly suitable for the state estimation problem, each with its advantages depending on the nature of the measurements' noise. However, there is not much focus on the models used for estimation. Examples of interesting sensors capable of obtaining important information that can be embedded are accelerometers, gyroscopes, magnetometers, and encoders, allowing the manipulator to estimate its state without the support of other external hardware. State estimation using only these kinds of sensors is considered automatic. Estimators designed for a specific application are often better at estimating the variables of interest for the context for which they were built; however, this means that they are not portable from one system to another. That is, if another manipulator is to be built with a different purpose, another estimator must be developed for this new context. Considering this problem, the estimators applied to the system are designed to be as modular and reusable as possible. To serve as a test-bed, an over-sensored manipulator is used, and the main goal of this redundancy is to correct the sensor's errors. Beyond that, the use of a system like the one mentioned also means that the developed models can be used in other manipulators. Throughout this article, the development process behind the presented estimators is described, as well as the developed test-bed manipulator. Section 2 presents the different models for manipulators and sensors.