Incorporating additional objectives, such as energy efficiency or mission completion, into the scenario-based MPC framework while maintaining probabilistic safety guarantees can be achieved through several adaptations:
Multi-Objective Optimization: The optimization problem can be reformulated as a multi-objective optimization problem, where the objectives of safety, energy efficiency, and mission completion are balanced. This can be done by introducing a weighted sum of the objectives or using Pareto optimization techniques to find a set of optimal solutions that trade off between conflicting objectives.
Energy-Aware Control Barrier Functions: The CBFs can be designed to include terms that account for energy consumption. For instance, the control inputs can be penalized based on their energy usage, encouraging the controller to select actions that minimize energy expenditure while still satisfying safety constraints.
Mission-Specific Constraints: Additional constraints can be integrated into the CBF framework that reflect mission-specific requirements. For example, constraints could be added to ensure that the agents reach their target positions within a certain time frame or that they follow a specific trajectory that optimizes mission completion.
Adaptive Weighting of Objectives: The weights assigned to different objectives can be made adaptive based on the current state of the system or the environment. For instance, during critical phases of a mission, safety might be prioritized, while in less critical phases, energy efficiency could be emphasized.
Hierarchical Control Structure: A hierarchical control structure can be implemented, where a high-level planner determines the mission objectives and a low-level controller ensures safety and energy efficiency. This separation allows for more complex mission planning while still adhering to safety constraints.
Probabilistic Guarantees for Additional Objectives: The framework can be extended to provide probabilistic guarantees not only for safety but also for the additional objectives. This could involve deriving new theoretical results that characterize the expected performance regarding energy consumption or mission completion times under the scenario-based approach.
By integrating these adaptations, the scenario-based MPC framework can effectively balance multiple objectives while ensuring that safety remains a top priority, thus enhancing the overall performance of autonomous systems in complex environments.