SAPPO is a high-precision, low-cost and highly scalable indoor localization system. The system is designed using modified HC-SR04 ultrasound transducers as a base to be used as distance meters between beacons and mobile robots. Additionally, it has a very unusual arrangement of its elements, such that the beacons and the array of transmitters of the mobile robot are located in very close planes, in a horizontal emission arrangement, parallel to the ground, achieving a range per transducer of almost 12 meters. SAPPO represents a significant leap forward in ultrasound localization systems, in terms of reducing the density of beacons while maintaining average precision in the millimeter range.

This work presents a three-dimensional geometric resolution method to calculate the complete inverse kinematics of a 7-degree-of-freedom articulated arm, including the hand itself. The method is classified as an analytical method with geometric solution, since it obtains a precise solution in a closed number of steps, converting the inverse kinematic problem into a three-dimensional geometric model. To simplify the problem, the kinematic decoupling method is used, so that the position of the wrist is calculated independently on one hand with information on the orientation of the hand, and the angles of the rest of the arm are calculated from the wrist.

This article describes a bipedal walking algorithm with inverse kinematics resolution based solely on geometric methods, so that all mathematical concepts are explained from the base, in order to clarify the reason for this solution. To do so, it has been necessary to simplify the problem and carry out didactic work to distribute content. In general, the articles related to this topic use matrix systems to solve both direct and inverse kinematics, using complex techniques such as decoupling or the Jacobian calculation. By simplifying the walking process, its resolution has been proposed in a simple way using only geometric techniques.