Academic journal article Memory & Cognition

Path Planning under Spatial Uncertainty

Academic journal article Memory & Cognition

Path Planning under Spatial Uncertainty

Article excerpt

In this article, we present experiments studying path planning under spatial uncertainties. In the main experiment, the participants' task was to navigate the shortest possible path to find an object hidden in one of four places and to bring it to the final destination. The probability of finding the object (probability matrix) was different for each of the four places and varied between conditions. Given such uncertainties about the object's location, planning a single path is not sufficient Participants had to generate multiple consecutive plans (metaplans)-for example: If the object is found in A, proceed to the destination; if the object is not found, proceed to B; and so on. The optimal solution depends on the specific probability matrix. In each condition, participants learned a different probability matrix and were then asked to report the optimal metaplan. Results demonstrate effective integration of the probabilistic information about the object's location during planning. We present a hierarchical planning scheme that could account for participants' behavior, as well as for systematic errors and differences between conditions.

Path Planning Under Spatial Uncertainty

The selection between path alternatives, and the planning of novel paths, are essential and frequent tasks for human navigators. Several studies have addressed the underlying cognitive strategies and mechanisms (e.g., Christenfeld, 1995; Gärling & Gärung, 1988; Golledge, 1995; Kölscher, Meilinger, Vrachliotis, Brösamle, & Knauff, 2006; Wiener & Mallot, 2003; Wiener, Schnee, & Mallot, 2004). All prior studies on path selection and path planning behavior assumed or stated that all required spatial information was available. In real life, however, navigators have to deal with incomplete or imprecise spatial knowledge resulting in spatial uncertainties. They might, for example, be confronted with situations in which the exact location of a goal or goal place is unknown, or can be judged with limited probability only. In this article, we intend to investigate the strategies and heuristics employed by navigators during path planning under such spatial uncertainties.

The main experimental task was analogous to the following scenario:

On your way home from work you realize that you are missing your keys. You know, however, that your roommate, who has another set of keys, has an appointment for dinner in a nearby restaurant after work. Obviously, the probability to find your roommate at work or in one of the restaurants depends on the time of day. Given different timings, what is the best path (i.e., in which order should you visit your roommate's workplace and the nearby restaurants) to find him/her, get the keys, and get home as quickly as possible?

What is being described here is a path planning task with a destination, and with an intermediate target whose exact whereabouts are uncertain but which can be described by a probability matrix over multiple locations. This probability matrix might change with different timings: If you leave work early, the probability of finding your roommate still at work is rather high. As time goes by, however, the probability of finding your roommate at work decreases, whereas the probability of finding him or her in a nearby restaurant increases.

Decision Making and Uncertainties

In the scenario described above, decisions have to be made about the order in which different locations are visited, although the exact whereabouts of the target can be described with only a certain limited probability. Probabilistic decision making has been extensively studied in nonspatial contexts in probability learning experiments, in which participants are faced with response alternatives that differ in terms of payoff (e.g., Shanks, Tunney, & McCarthy, 2002; West & Stanovich, 2003). Alternative A, for example, is rewarded in 70% of the choices, whereas Alternative B is rewarded in 30% of the choices. …

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