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

In communicationless environments, multi-robot systems must operate without the constant information exchange that many coordination strategies typically assume. This paper presents a novel dynamic epistemic planning framework that enables implicit coordination and long horizon planning through higher-order reasoning among robots. With our approach, robots form and propagate higher-order belief particles, update world beliefs using Bayesian inference, and select actions via a behavior tree that anticipates teammates' likely decisions. A temporally aware Model Predictive Path Integral (MPPI) controller integrates this reasoning into low-level execution, allowing robots to plan intercepts and adapt trajectories under partial observability. The proposed framework is evaluated in both simulations and physical experiments, where it consistently reduces task completion time compared to a first-order baseline, demonstrating that epistemic logic can serve as a robust foundation for resilient coordination in communication-restricted domains.

This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge from observations, and the optimal course of action depends on these observations. \revise{Trajectory-trees, optimized in belief space, naturally capture this dependency by branching where the belief state is expected to evolve into multiple distinct scenarios, such as upon receiving an observation. Unlike sequential trajectories, which model a single forward evolution of the system, trajectory-trees capture multiple possible contingencies.} First, we focus on Model Predictive Control (MPC) and demonstrate the benefits of planning tree-like trajectories. We formulate the control problem as the optimization of a tree with a single branching (PO-MPC). This improves performance by reducing control costs through more informed planning. To satisfy the real-time constraints of MPC, we develop an optimization algorithm called Distributed Augmented Lagrangian (D-AuLa), which leverages the decomposability of the PO-MPC formulation to parallelize and accelerate the optimization. We apply the method to both linear and non-linear MPC problems using autonomous driving examples. Second, we address Task And Motion Planning (TAMP), and introduce a planner (PO-LGP) reasoning on decision trees at task level, and trajectory-trees at motion-planning level. This approach builds upon the Logic-Geometric-Programming Framework (LGP) and extends it to partially observable problems. The experiments show the method's applicability to problems with a small belief state size, and scales to larger problems by optimizing explorative policies, which are used as macro-actions in an overarching task plan.

Robots operating in cluttered environments must often manipulate objects whose locations are only partially observable. A central challenge is deciding whether to acquire another observation or to first manipulate objects that may occlude the target. Conventional task and motion planning (TAMP) approaches typically make this decision using symbolic action costs or expensive geometric planning, neither of which adequately captures how likely an observation is to reveal an occluded target. We introduce Imagine-TAMP, an interleaved planning and execution framework that uses semantic and geometric imagination to compare alternative task-level strategies under partial observability before committing to expensive motion planning. A vision-language model shapes a particle belief over target locations using commonsense relationships between the target and visible objects, while a generative scene model estimates plausible geometry in unobserved regions. Given a target hypothesis and imagined scene, Imagine-TAMP generates multiple symbolic plan skeletons and assigns non-unit costs that approximate both manipulation effort and target visibility from sensing actions, distinguishing a short but poorly informative observation strategy from a longer strategy that first manipulates an occluder to better expose the target. The selected skeleton is then refined into a feasible continuous plan and executed, with new observations updating the belief and triggering replanning when necessary. Experiments show that imagination-guided evaluation improves observation-versus-manipulation decisions: in viewpoint-constrained shelf scenes, non-unit geometric evaluation increases success from 46.0% to 84.0%, while semantic belief shaping further reduces manipulation and replanning. On a real robot, the complete system reduces planning time by 32% relative to a geometry-only ablation.