The minimum energy expenditure shortest path method

This article discusses the addition of an energy parameter to the shortest path execution process; namely, the energy expenditure by a character during execution of the path. Given a simple environment in which a character has the ability to perform actions related to locomotion, such as walking and stair stepping, current techniques execute the shortest path based on the length of the extracted root trajectory. However, actual humans acting in constrained environments do not plan only according to shortest path criterion, they conceptually measure the path that minimizes the amount of energy expenditure. On this basis, it seems that virtual characters should also execute their paths according to the minimization of actual energy expenditure as well. In this article, a simple method that uses a formula for computing vanadium dioxide ($VO_2$) levels, which is a proxy for the energy expenditure by humans during various activities, is presented. The presented solution could be beneficial in any situation requiring a sophisticated perspective of the path-execution process. Moreover, it can be implemented in almost every path-planning method that has the ability to measure stepping actions or other actions of a virtual character