Robotics has been supplemented by the growing body of techniques associated with formal languages. One remaining challenge for bottom-up formal methods is to provide effective abstractions to their top-down counterparts in order to achieve a seamless integration. This paper describes our efforts to tackle this challenge in the domain of spatial behavior. Our general goal is to understand principles involved in the formation of hierarchic representations that can greatly simplify the control and planning tasks. We propose that this hierarchy be built from the bottom-up according to formal language principles, while incorporating principles from dynamical systems theory. The general idea is that relevant interactions between the agent's dynamics, task and environment are manifested as patterns. Compared to other approaches these patterns are not based on abstract, high-level constructs but convey a form of meaning that inherently ties the system's dynamics, environment and task characteristics. Understanding the natural principles underlying hierarchic organization of behavior is a fundamental step toward developing formal languages dealing with dynamical systems. It can be applied to help understand spatial intelligence and eventually help design more versatile and adaptive agents.

Humans are capable of agile and adaptive spatial behaviors that are far beyond the capabilities of today's autonomous systems. Spatial behaviors have been investigated in AI, cognitive science and neuroscience. This paper describes an engineering-oriented perspective that is intended to bridge the gap between these fields. We claim that spatial behavior cannot be fully understood by considering the agent and its environment separately. In our approach, we put the emphasis on the interaction between the agent's dynamics and the task environment. We hypothesize that specific patterns emerge from this interaction and that these patterns are used by human operators to mitigate the complexity involved in agile and adaptive spatial performance. This paper describes preliminary experiments and a methodology to investigate these hypotheses.

Autonomous estimation of the altitude of an Unmanned Aerial Vehicle (UAV) is extremely important when dealing with flight maneuvers like landing, steady flight, etc. Vision based techniques for solving this problem have been underutilized. In this paper, we propose a new algorithm to estimate the altitude of a UAV from top-down aerial images taken from a single on-board camera. We use a semi-supervised machine learning approach to solve the problem. The basic idea of our technique is to learn the mapping between the texture information contained in an image to a possible altitude value. We learn an over complete sparse basis set from a corpus of unlabeled images capturing the texture variations. This is followed by regression of this basis set against a training set of altitudes. Finally, a spatio-temporal Markov Random Field is modeled over the altitudes in test images, which is maximized over the posterior distribution using the MAP estimate by solving a quadratic optimization problem with L1 regularity constraints. The method is evaluated in a laboratory setting with a real helicopter and is found to provide promising results with sufficiently fast turnaround time.

In this paper we describe a study of the human pilot control behavior in a planar goal directed flight task. The experimental data was collected using a miniature helicopter in an indoor flight test facility. To provide insight into the human's control behavior we developed a technique to extract extremal fields from the family of collected trajectories. These fields describe the spatial distribution of the vehicle states and cost- to-go, including their statistical distribution, which provides information about the variability of the pilot's control behavior over the task domain. Once extracted we can compare these fields to the value functions obtained from the task's equivalent optimal control problem. The comparison of the human-extracted and the computed value function maps suggests that on average, the human acts similarity to an optimal control policy. The results also suggests that a simple mass-point model used for our analysis, and motivated by the hypothesis that the pilot acts as a dynamic inverse controller, is sufficient to explain the pilot's performance at the planning level. We use these results to develop hypotheses about human planning and control processes and discuss their biological plausibility based on control-theoretic interpretations. We plan to use the new insights from this framework to help design more capable and versatile algorithms for autonomous vehicle control, as well as help design man-machine interfaces that enable a more natural link with the operator's internal control and planning processes.