To extend the proposed framework to handle stochastic dynamics and uncertainties in the multi-agent trajectory game, we can incorporate probabilistic models and uncertainty quantification techniques. Here are some key steps to achieve this:
Stochastic Modeling: Introduce stochastic elements into the system dynamics to account for uncertainties in the environment and agent behaviors. This can be done by incorporating probabilistic distributions for state transitions and control inputs.
Robust Optimization: Modify the trajectory planning algorithm (STP) to optimize trajectories under uncertainty. This can involve robust optimization techniques that aim to find solutions that are resilient to variations in the system parameters.
Chance Constraints: Implement chance constraints to ensure that safety and performance requirements are met with a certain probability. This involves formulating constraints that need to hold true with a specified likelihood under the stochastic dynamics.
Stochastic Optimization: Utilize stochastic optimization methods to find optimal strategies under uncertainty. This involves considering the probabilistic nature of the system dynamics and making decisions that maximize expected performance.
Monte Carlo Simulation: Conduct Monte Carlo simulations to evaluate the performance of the system under different stochastic scenarios. This can help in understanding the impact of uncertainties on the overall system behavior.
By incorporating these techniques, the framework can effectively handle stochastic dynamics and uncertainties in the multi-agent trajectory game, providing robust and reliable solutions in real-world scenarios.