# Controlling Remotely Operated Vehicles with Deterministic Artificial Intelligence
## 1 Introduction  
Unmanned vehicles are increasingly popular in society and have proven especially useful in dangerous environments. Exploring for life deep at the bubbling chimneys of magma-heated water in the very deep, dark depths of the ocean [1] acts as prototype practice for deep space exploration by such unmanned systems as depicted in Figure 1. Planning to explore distant planets and moons such as Europa and Enceladus, the National Aeronautics and Space Administration (NASA) uses the BRUIE underwater rover to practice looking for life under the ice in Antarctica. The BRUIE rover is depicted in Figure 2 in an Arctic lake near Barrow, Alaska in 2015 [2]. Such dangerous environments illustrate the importance of highly capable, advanced systems automating as much activity as possible. The popularity of using such vehicles is due in part to their very long history of technological understanding and development, being governed by fundamental principles developed hundreds of years ago. Vehicle translation is governed by principles developed by [PERSON] in 1687 [3], while rotation is governed by principles elaborated by [PERSON] in 1776 [4]. The two natures of motion (translation and rotation) were expressed very early by [PERSON] in 1830 [5] as coupled and nonlinear and shortly afterwards embodied by [PERSON] in a now famous theorem [6]. [PERSON] introduced alternative formulation methods in 1834 using energy [7], while [PERSON] introduced a presentation using energy that more closely resembled [PERSON]'s original formulation [8, 9], and in the last century [PERSON] [10, 11, 12] provided the latest parameterization of the same natural relationships very often referred to as a Lagrangian formulation [8, 9] of [PERSON] principle, which was introduced in 1743 and published in 1747 [13; 14] and 1750 [15]. These fundamental and now well-understood principles of mechanics embodied the approaches to control themselves in an open-loop, feedforward sense, as expressed in the 1950's and 1960's, respectively, by [PERSON] in the West [16] and [PERSON] in the East [17]. [PERSON]'s work particularly applied to highly flexible robotic vehicles [18] sprung from their foundation of the core principles of adaptive techniques late in the last century [19; 20; 21]. A recent lineage of adaptive controls applied to robotic systems [19; 20] and spacecraft [21; 23] illustrated an ability to autonomously recover from significant damage without assistance [24]. The foundation of those methods was unique manifestations of the governing differential equations of motion in a feedforward fashion as controls, augmented with classical feedback rules used to adapt the feedforward controls. Highlighting and amplifying this foundation, [PERSON]. [25] demonstrated feedforward controls comprised of the governing differential equations of motion driven by autonomously generated trajectory commands was superior to linear-quadratic optimal feedback control. Later, [PERSON]. [26] developed optimal (in a two-norm sense) feedback to realize adaption, replacing the former adaptive methods based in classical feedback. In 2020, the combined method, newly labeled deterministic artificial intelligence [27], comprised of self-awareness statements (the feedforward codification of the governing differential equations) plus optimal learning (through feedback), was applied to unmanned ocean vehicles [27] as an embodied update to classical [28] and optimal (so-called \"modern\") approaches [29]. Deterministic artificial intelligence [27] is thus an alternative to adaptive control [19; 20; 21; 23; 24] and classical control schemes [28] and is based on the observation that, if one can discern the governing mathematical equations for a system (using any of the cited approaches [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]),  
Figure 1: NASA remotely operated vehicle sampling deep sea black smokers [1]. Image used for educational purposes in accordance with NASA Media Usage Guidelines [22].