Humanoid Robotic System with and without Elasticity Elements Walking on an Immobile/Mobile Platform

This work is concerned with the modeling and analysis of a complex humanoid robotic system walking on an immobile/mobile platform. For this purpose, a software package was synthesized which allows one to select configuration of both the humanoid and the platform. Each joint of the biped and platform can be defined by the user via the motor state (active or locked) and gear type (rigid or elastic). The user can also form very diverse configurations of the humanoid and platform. The software package forms a mathematical model. By selecting system’s parameters the simulation allows user to analyze dynamic behavior of the biped of selected configuration, walking on either an immobile or mobile platform of selected configuration. In the moment when the biped steps on the platform, the latter, by its dynamics, acts on the biped dynamics, and the biped on the other hand, by its characteristics, influences dynamics of the platform motion. These two complex contacting systems form a more complex system, whose mathematical model has to encompass all the elements of coupling between the humanoid joints and platform joints. The phenomenon of coupling is analyzed first on a humanoid robotic system with all rigid elements, which is in contact with the platform mechanism having also all rigid elements. It has been shown that coupling is more influenced when elasticity elements are included into the configuration. Insufficient knowledge of coupling characteristics may present a serious disturbance to the system in the robotic task realization. The deviation of the ZMP (Zero-Moment Point) from the reference trajectory is presented, which implies the need for the synthesis of new control structures for stabilizing biped motion on the immobile/mobile platform. The reference trajectory may be defined in very different ways and from several aspects. Reference trajectory of each joint can be defined so to encompass or not encompass elastic deformations. The control structure for the biped walking on the platform should be defined so that it satisfies the requirement for the ZMP to be within the given boundaries in every sampling instant, which guarantees dynamic balance of the locomotion mechanism in the real regime. The control is defined as CR (Centralized Reference control, calculated from the reference state), plus LO (control via local feedbacks of motor motion with respect to position and velocity). In the case of the biped motion on a mobile platform CR control is defined separately under the real conditions of unknown characteristics of coupling between the two complex systems, as well as unknown elasticity properties. The analysis of simulation results of the humanoid robot motion on a mobile platform gives evidence for all the complexity of this system and shows how much system parameters (choice of trajectory, configuration, geometry, elasticity characteristics, motor, etc.) influence stabilization of its humanoid motion.