Bi-Objective Trail Planning for a Robot Team Navigating a Hazardous Environment

Centrala begrepp

The key objective is to plan the trails of a robot team in a hazardous environment to maximize the expected team reward and the expected number of surviving robots, which are inherently conflicting goals.

Sammanfattning

The content discusses the bi-objective team orienteering in hazardous environments (BOTOHE) problem, where a team of mobile robots navigate a hazardous environment modeled as a directed graph. Each node in the graph offers a reward to the team if visited by a robot, but traversing the arcs (edges) presents known probabilities of robot destruction.

The two objectives are to maximize the expected team reward and the expected number of robots that survive the mission. These objectives are inherently conflicting, as robots must risk their survival to visit high-reward nodes. The authors employ bi-objective ant colony optimization to search for the Pareto-optimal set of robot-team trail plans, which can then be presented to a human decision-maker to select the plan that balances reward and robot survival according to their preferences.

The key highlights include:

• Modeling the hazardous environment as a directed graph with known arc survival probabilities
• Formulating the bi-objective optimization problem to maximize expected team reward and expected robot survival
• Employing bi-objective ant colony optimization to efficiently search for the Pareto-optimal set of robot-team trail plans
• Visualizing the pheromone trails and Pareto-optimal solutions to gain intuition
• Conducting ablation studies to quantify the importance of heuristics and pheromone in guiding the search

Statistik

"Teams of mobile [aerial, ground, or aquatic] robots have applications in resource de-livery, patrolling, information-gathering, agriculture, forest fire fighting, chemical plume source localization and mapping, and search-and-rescue."
"Robots traversing a hazardous environment should plan and coordinate their trails in consideration of risks of failure, destruction, or capture."

Citat

"Herein, we consider bi-objective trail-planning for a mobile team of robots orienteering in a hazardous environment."
"Because the bi-objective optimization problem in eqn. 1 presents a conflict between de-signing the robot-team trail plan to maximize the expected reward and the number of surviving robots, we seek the Pareto-optimal set of team-robot trail plans."

Viktiga insikter från

Bi-objective trail-planning for a robot team orienteering in a hazardous environment

by Cory M. Simo... på arxiv.org 09-19-2024

https://arxiv.org/pdf/2409.12114.pdf

Djupare frågor

How could the BOTOHE problem be extended to handle heterogeneous robot teams with different capabilities and survival probabilities?

To extend the Bi-Objective Team Orienteering in Hazardous Environments (BOTOHE) problem for heterogeneous robot teams, we can introduce several modifications that account for the varying capabilities and survival probabilities of each robot.

Capability Differentiation: Each robot can be assigned specific capabilities that affect its ability to collect rewards from nodes. For instance, some robots may be equipped with advanced imaging technology that allows them to gather higher-quality data from certain nodes, thus yielding greater rewards. This can be modeled by associating different reward multipliers with each robot based on its capabilities when visiting nodes.

Variable Survival Probabilities: The survival probabilities for each robot can be made dependent on their characteristics, such as speed, stealth, or armor. For example, a faster robot might have a lower survival probability when traversing certain hazardous arcs due to its exposure time, while a stealthier robot might have a higher survival probability in the same environment. This can be implemented by modifying the arc survival probability map to include robot-specific survival probabilities, denoted as ω_k(v, v′) for robot k.

Trail Planning: The trail planning algorithm must account for the different capabilities and survival probabilities of the robots. This could involve a multi-objective optimization approach where the expected reward and survival are calculated for each robot based on its unique attributes. The ant colony optimization (ACO) algorithm can be adapted to allow each worker ant to represent a different robot type, thus exploring the Pareto-optimal set of trail plans that maximize the overall team reward while ensuring a certain level of survival across the heterogeneous team.

Cooperative Strategies: The robots can be programmed to adopt cooperative strategies that leverage their strengths. For instance, a more capable robot could take on riskier paths to collect high-value rewards, while less capable robots could focus on safer routes, ensuring that the overall team objective is met without compromising individual robot survival.

By integrating these elements, the BOTOHE problem can effectively accommodate heterogeneous robot teams, enhancing their operational efficiency in hazardous environments.

How could the BOTOHE problem be modified to consider more complex reward structures, such as time-dependent, stochastic, or non-additive rewards?

Modifying the BOTOHE problem to incorporate more complex reward structures involves several key adjustments to the reward calculation and optimization framework:

Time-Dependent Rewards: To account for time-dependent rewards, the reward function r(v) can be modified to include a temporal component, r(v, t), where t represents the time at which a robot visits node v. This could reflect scenarios where the value of the reward diminishes over time, such as in resource delivery missions where the urgency of delivery affects the reward. The optimization algorithm would need to track the time taken for each robot to complete its trail and adjust the expected rewards accordingly.

Stochastic Rewards: To incorporate stochastic rewards, we can model the rewards as random variables rather than fixed values. Each node could have a probability distribution associated with its reward, reflecting the uncertainty in the reward that can be obtained upon visiting. The expected reward for each node would then be calculated as the mean of its probability distribution, and the optimization algorithm would aim to maximize the expected total reward across all nodes visited by the robot team.

Non-Additive Rewards: Non-additive rewards can be introduced by allowing the rewards from multiple visits to the same node to interact in complex ways. For example, visiting a node multiple times could yield diminishing returns or even negative synergy effects if certain conditions are met (e.g., over-saturation of data). This can be modeled by defining a reward function that takes into account the number of visits to each node and applies a non-linear transformation to the total reward based on the visitation count.

Dynamic Reward Structures: The reward structure can also be made dynamic, where the rewards change based on the actions of the robots or the state of the environment. For instance, if a robot is detected by an adversary, the rewards for nearby nodes could decrease, reflecting the increased risk. The optimization algorithm would need to adapt in real-time to these changes, potentially using reinforcement learning techniques to update the reward expectations based on observed outcomes.

By implementing these modifications, the BOTOHE problem can effectively handle complex reward structures, leading to more realistic and adaptable robot team strategies in hazardous environments.

How could the survival probabilities associated with the graph edges be learned or updated from data over repeated missions?

Learning or updating the survival probabilities associated with the graph edges in the BOTOHE problem can be approached through a data-driven framework that incorporates machine learning techniques. Here are several strategies to achieve this:

Bayesian Inference: A Bayesian approach can be employed to model the uncertainty in survival probabilities. Initially, a prior distribution can be assigned to each edge's survival probability ω(i, j). As robots complete missions, the outcomes (survived or destroyed) can be used to update these probabilities using Bayes' theorem. This allows for a continuous refinement of the survival probabilities based on empirical data collected during missions.

Reinforcement Learning: Reinforcement learning (RL) can be utilized to adaptively learn survival probabilities. An RL agent can be trained to explore the environment and learn the survival outcomes associated with different paths. The agent would receive rewards based on successful traversals and penalties for failures, allowing it to update its estimates of survival probabilities over time. This approach can be particularly effective in dynamic environments where conditions may change between missions.

Statistical Learning Models: Machine learning models, such as logistic regression or decision trees, can be trained on historical mission data to predict survival probabilities based on various features, such as the characteristics of the edges (e.g., terrain type, presence of adversaries) and the context of the mission (e.g., time of day, robot type). These models can be updated as new data becomes available, improving their predictive accuracy.

Data Fusion Techniques: Combining data from multiple missions can enhance the robustness of survival probability estimates. Techniques such as ensemble learning can be employed to aggregate predictions from different models or sources of data, leading to more reliable estimates. Additionally, sensor data from the robots during missions can be integrated to provide real-time updates to survival probabilities based on observed conditions.

Feedback Loops: Implementing feedback loops where the outcomes of missions inform future planning can create a self-improving system. For instance, if certain paths consistently result in robot destruction, the survival probabilities for those edges can be adjusted downward, while successful paths can have their probabilities increased. This adaptive mechanism ensures that the robot team learns from experience and optimizes its trail planning accordingly.

By employing these strategies, the survival probabilities associated with the graph edges can be effectively learned and updated, leading to improved decision-making and enhanced performance of robot teams operating in hazardous environments.