4D-based Robot Navigation Using Relativistic Image Processing

TL;DR

This paper presents a 4D-based approach to robot navigation using relativistic image processing, which expands the causal understanding and the resulting interaction radius of a robot through the use of visual and sensory 4D information.

Abstract

Machine perception is an important prerequisite for safe interaction and locomotion in dynamic environments. This requires not only the timely perception of surrounding geometries and distances but also the ability to react to changing situations through predefined, learned but also reusable skill endings of a robot so that physical damage or bodily harm can be avoided. In this context, 4D perception offers the possibility of predicting one's own position and changes in the environment over time. In this paper, we present a 4D-based approach to robot navigation using relativistic image processing. Relativistic image processing handles the temporal-related sensor information in a tensor model within a constructive 4D space. 4D-based navigation expands the causal understanding and the resulting interaction radius of a robot through the use of visual and sensory 4D information.

Figures (8)

• Figure 1: The trajectory, adapted and reproduced from MK.22, demonstrates the sensor-acquired climbing of stairs in an Euclidean diagram. The black arrows represent the sensor orientation, the red dots represent the calculated position.
• Figure 2: This figure illustrates the tensor-based reference diagram. The novel 4D diagram converts Euclidean coordinates into spatio-temporal coordinates by composing tensor bases.
• Figure 3: The figure illustrates 10-DoF Motion in the Model of Schlingel Diagram. In the dynamic state, motion occurs within all 6 planes. The motion itself is demonstrated by 4 translations and 6 rotations.
• Figure 4: The illustration shows the design of sensor estimated 4D-positioning. The respective rotation and translation can be calculated from IMU-specific acceleration, angular velocities, and magnetic fields. By applying the Lorentz factor, the temporal translation and rotations can be determined. The resulting 4D translation and rotation can be expressed as a 4D position in the form of the four-vector $\chi$.
• Figure 5: The pyramid-shaped illustration shows the structure of sensor and camera-related inertial systems. Information from different sensors of an intrinsic inertial system [$\mathbb{R}_{s,i}$,$\mathbb{R}_{c,i}$] can be transferred to extrinsic inertial systems [$\mathbb{R}_{s}$,$\mathbb{R}_{s}$] and a higher-level world coordinate system $\mathbb{R}_{w}$ via referenceable variables.