From Legible to Inscrutable Trajectories: (Il)legible Motion Planning Accounting for Multiple Observers

TL;DR

The paper tackles legible motion planning under mixed motives and limited observability by formalizing the Mixed-Motive Limited-Observability Legible Motion Planning (MMLO-LMP) problem and introducing the DUBIOUS trajectory optimizer. It integrates observer-specific visibility regions and motives into a unified optimization framework based on STOMP, balancing legibility for cooperative observers with illegibility for adversarial ones. Key contributions include formal problem definition, a tractable optimization approach, and extensive evaluations across scenarios with overlapping visibility and diverse observer motives, demonstrating strategies such as decoy and ambiguous illegibility. The work advances safe and strategic motion planning in environments where observers have partial views and conflicting intents, with practical implications for human-robot collaboration, security, and competitive settings; future work envisions moving observers, observer teamwork, and online adaptations.

Abstract

In cooperative environments, such as in factories or assistive scenarios, it is important for a robot to communicate its intentions to observers, who could be either other humans or robots. A legible trajectory allows an observer to quickly and accurately predict an agent's intention. In adversarial environments, such as in military operations or games, it is important for a robot to not communicate its intentions to observers. An illegible trajectory leads an observer to incorrectly predict the agent's intention or delays when an observer is able to make a correct prediction about the agent's intention. However, in some environments there are multiple observers, each of whom may be able to see only part of the environment, and each of whom may have different motives. In this work, we introduce the Mixed-Motive Limited-Observability Legible Motion Planning (MMLO-LMP) problem, which requires a motion planner to generate a trajectory that is legible to observers with positive motives and illegible to observers with negative motives while also considering the visibility limitations of each observer. We highlight multiple strategies an agent can take while still achieving the problem objective. We also present DUBIOUS, a trajectory optimizer that solves MMLO-LMP. Our results show that DUBIOUS can generate trajectories that balance legibility with the motives and limited visibility regions of the observers. Future work includes many variations of MMLO-LMP, including moving observers and observer teaming.

Figures (5)

• Figure 1: An example of a legible and a decoy-legible trajectory. These baselines are generated with DUBIOUS in an environment that assumes full observability for a single +1 or -1 observer, for the max legible and max decoy illegible trajectories, respectively. The decoy trajectory is an example of the $\textsc{Illegible-decoy}$ strategy. Note that the legible trajectory curves away from the other goal options, reducing the probability that the other goals are the true goal. Conversely, note that the illegible trajectory moves toward the other opponents before curving toward its correct goal.
• Figure 2: STOMP Over-optimization. As the number of iterations increases, STOMP creates increasingly extreme trajectories. Here we show legible trajectories generated through the region in view of an observer with motive (green) +1 at iterations 80, 480, 700, and 1000.
• Figure 3: (Top) Environments with one observer with partial legibility. Solid lines are baseline planners. Fig. \ref{['fig:partial_view:leg']} has one observer with +1 motive that can see the agent when it is in the green box. Fig. \ref{['fig:partial_view:illeg']} has one observer with -1 motive that can see the agent's location when it is in the red box. (Bottom) Probabilities $P(G_i|\xi_{S\rightarrow\xi(t)})$ for each goal, over time, for select trajectories.
• Figure 4: An environment with 4 observers, motive values +1, +0.25, -0.25, and -1, with multiple overlapping visibility regions. Green regions are visible to positive observers with higher opacity indicating higher motive values. Red regions are visible to negative observers with higher opacity indicating lower motive values.
• Figure 5: Both figures illustrate multi-observer environments with overlapping visibility regions. In Fig. \ref{['fig:box-in-box:good-in-bad']}, the visibility region of a +1 observer is completely covered by the visibility region of a -0.25 observer. In Fig. \ref{['fig:box-in-box:bad-in-good']}, the visibility region of a -1 observer is completely covered by the visibility region of a +0.25 observer.