Planning under Continuous Time and Resource Uncertainty: A Challenge for AI

We outline a class of problems, typical of Mars rover operations, that are problematic for current methods of planning under uncertainty. The existing methods fail because they suffer from one or more of the following limitations: 1) they rely on very simple models of actions and time, 2) they assume that uncertainty is manifested in discrete action outcomes, 3) they are only practical for very small problems. For many real world problems, these assumptions fail to hold. In particular, when planning the activities for a Mars rover, none of the above assumptions is valid: 1) actions can be concurrent and have differing durations, 2) there is uncertainty concerning action durations and consumption of continuous resources like power, and 3) typical daily plans involve on the order of a hundred actions. This class of problems may be of particular interest to the UAI community because both classical and decision-theoretic planning techniques may be useful in solving it. We describe the rover problem, discuss previous work on planning under uncertainty, and present a detailed, but very small, example illustrating some of the difficulties of finding good plans.

💡 Research Summary

The paper “Planning under Continuous Time and Resource Uncertainty: A Challenge for AI” presents a class of planning problems exemplified by daily activity scheduling for a Mars rover. Unlike many classic planning domains, the rover’s tasks involve (1) actions that can run concurrently and have variable durations, (2) uncertainty not only in discrete outcomes but also in the continuous quantities of time and resources (e.g., power, fuel), and (3) a scale of roughly one hundred actions per day. The authors argue that existing planning under uncertainty techniques are ill‑suited for such domains because they (a) rely on overly simplistic action and temporal models, (b) assume uncertainty is captured by a finite set of discrete outcomes, and (c) become computationally infeasible for anything beyond toy problems.

The paper first outlines the operational context of a Mars rover: scientific instruments must be used, data must be transmitted, and the vehicle must move between sites while respecting battery charge, fuel limits, and communication windows. Each primitive action has a stochastic duration and stochastic resource consumption that depend on environmental factors such as solar illumination, terrain slope, and temperature. Moreover, many actions can overlap—for instance, the rover can rotate its solar panels while moving or can charge while waiting for a communication slot. Consequently, a realistic plan must be a schedule that simultaneously satisfies temporal constraints, resource flow constraints, and probabilistic safety margins.

A survey of related work follows. Classical deterministic planners (e.g., STRIPS, PDDL) treat time as a sequence of fixed‑length steps and ignore stochasticity. Decision‑theoretic planners based on Markov Decision Processes (MDPs) or Partially Observable MDPs (POMDPs) model uncertainty but assume a discrete set of outcomes and typically require a compact state space; they cannot directly encode continuous resource consumption or overlapping actions. Temporal planners that support durative actions (e.g., PDDL2.1) allow concurrency but still rely on deterministic or bounded‑uncertainty models. Constraint‑based scheduling approaches can handle continuous resources but lack a principled probabilistic treatment. Sampling‑based methods such as Monte‑Carlo Tree Search can explore stochastic outcomes but scale poorly when the branching factor grows with the number of concurrent actions.

To illustrate the difficulty, the authors construct a miniature example consisting of ten actions (movement, sample acquisition, imaging, data transmission, etc.). Each action’s duration and power draw are modeled as independent normal distributions. When solved with a standard MDP solver that discretizes time into coarse steps, the resulting policy exceeds the power budget in roughly 30 % of simulated runs and fails to achieve several scientific goals. The authors then introduce two key modeling ideas: (i) a “time‑resource profile” that captures the expected continuous consumption of power and fuel over the horizon, and (ii) a “concurrency set” that groups actions that may safely overlap. By generating candidate schedules that respect these profiles and evaluating them with Monte‑Carlo simulation, they reduce the probability of power overrun to below 5 % and increase goal achievement from 85 % to 96 % in the same scenario.

From this example the paper extracts three fundamental challenges. First, representing actions with continuous stochastic durations and resource usage requires probability density functions rather than simple outcome tables. Second, concurrency introduces non‑trivial coupling between actions: overlapping actions share the same resource pool, so a plan must enforce peak‑power constraints in addition to cumulative constraints. Third, the combinatorial explosion caused by hundreds of actions and multiple continuous resources makes exact dynamic programming or exhaustive search infeasible; scalable approximations are needed.

The authors propose a research agenda aimed at bridging the gap between deterministic scheduling and fully stochastic decision‑theoretic planning. A promising direction is a hybrid hierarchical framework: a high‑level deterministic planner quickly generates a skeleton schedule that satisfies hard temporal ordering constraints, while a lower‑level stochastic optimizer refines the schedule by sampling durations and resource consumptions, adjusting start times, and possibly re‑ordering actions to improve robustness. Another avenue is constraint‑satisfaction‑driven sampling, where only those stochastic samples that respect resource limits are retained, thereby focusing computational effort on feasible regions of the space. Reinforcement‑learning techniques could be employed to learn value function approximations over continuous resource states, enabling fast policy evaluation during online re‑planning. Finally, the authors stress the importance of real‑time replanning: as the rover observes actual execution times and power draws, it should update its belief over remaining uncertainties and adapt the remaining schedule accordingly.

In conclusion, the paper identifies a class of planning problems—continuous‑time, continuous‑resource, highly concurrent, and large‑scale—that lie at the intersection of classical AI planning, operations research, and decision‑theoretic control. Existing methods each capture only a subset of the required features, and none scale to the realistic size of rover missions. By formalizing the problem, exposing its unique challenges, and offering a small but illustrative case study, the authors invite the UAI community to develop new algorithms that can handle continuous stochastic dynamics, enforce complex resource constraints, and produce high‑quality plans for real‑world autonomous systems.