Foraging theory for autonomous vehicle speed choice

Abstract

We consider the optimal control design of an abstract autonomous vehicle (AAV). The AAV searches an area for tasks that are detected with a probability that depends on vehicle speed, and each detected task can be processed or ignored. Both searching and processing are costly, but processing also returns rewards that quantify designer preferences. We generalize results from the analysis of animal foraging behavior to model the AAV. Then, using a performance metric common in behavioral ecology, we explicitly find the optimal speed and task processing choice policy for a version of the AAV problem. Finally, in simulation, we show how parameter estimation can be used to determine the optimal controller online when density of task types is unknown.

Introduction

Consider a vehicle that searches through a territory for tasks, and let probability of task detection depend on vehicle speed (e.g., sensor bandwidth or hysteresis requirements may prevent detections at high search speeds). On detecting a task, the vehicle may choose to process it. Both searching and processing are costly (e.g., monetary cost of depleted vehicle fuel), and search costs depend on search speed. However, the designer rewards the vehicle for processing. Hence, good vehicle control policies will set search speed and determine tasks to process in a way that balances rewards and costs.

Our vehicle description fits a variety of robotics, queueing, and other engineering applications well (e.g., Quijano et al., 2006; Passino, 2002, Passino, 2005), and so we refer to it as an abstract autonomous vehicle (AAV). The AAV is a generalization of the solitary forager from optimal foraging theory (Stephens and Krebs, 1986). Optimal foraging theorists assume that natural selection results in behaviors that optimize Darwinian fitness, and so they use analysis of proximate fitness functions to explain observed behaviors in nature. Lately, methods from optimal foraging theory have been used to analyze human behavior in nature (e.g., Rowcliffe et al., 2004) and on the Internet (Pirolli and Card, 1999; Pirolli, 2005, Pirolli, 2007). Following the example of Andrews et al., 2004, Andrews et al., 2007, we apply similar methods to AAV policy design.

Early foraging theory by Schoener (1971) postulates that optimal behaviors are found on a continuum with foraging time minimization and net energetic intake maximization at opposite ends. These strategies allow time for other activities (e.g., predator avoidance and reproduction) while preventing starvation. Later, Pyke et al. (1977) argue that lifetime energetic rate maximization is consistent with this idea, and Charnov and Orians (1973) develop several rate maximization models that continue to be used today (Charnov, 1976a, Charnov, 1976b; Stephens and Krebs, 1986). As discussed by Houston and McNamara (1999), rate maximization is equivalent to minimizing the opportunity cost of each foraging decision. In our context, foraging is equivalent to task processing, and so net energetic intake is equivalent to net reward gained. Hence, we develop AAV policies that maximize long-term net rate of reward.

The present work combines and extends work by Andrews et al. (2004), which extends foraging theory to engineering, and Gendron and Staddon (1983), which modifies standard foraging models to include speed effects. Our AAV model subsumes those models while also including more general search and processing costs. Under mild assumptions on detection probabilities, we give an analytical solution for the optimal AAV behavior in an environment with an arbitrary number of task types. Additionally, we use computer simulation to show how online parameter estimation leads to convergence to the optimal AAV policy. While this more general AAV model can be useful in ecological analysis, we focus on its application to engineering design.

The remainder of this paper is organized as follows. In 2 Simple AAV model, 3 Speed-dependent AAV model, the foraging-based AAV model is presented. Analytical optimization results are given in Section 4, and these results are validated using results from a fixed-wing airborne vehicle simulation in Section 5. Finally, in Section 6, we make some concluding remarks and suggestions for future work.