Risk-aware Spatio-temporal Logic Planning in Gaussian Belief Spaces

In many real-world robotic scenarios, we cannot assume exact knowledge about a robot's state due to unmodeled dynamics or noisy sensors. Planning in belief space addresses this problem by tightly coupling perception and planning modules to obtain trajectories that take into account the environment's stochasticity. However, existing works are often limited to tasks such as the classic reach-avoid problem and do not provide risk awareness. We propose a risk-aware planning strategy in belief space that minimizes the risk of violating a given specification and enables a robot to actively gather information about its state. We use Risk Signal Temporal Logic (RiSTL) as a specification language in belief space to express complex spatio-temporal missions including predicates over Gaussian beliefs. We synthesize trajectories for challenging scenarios that cannot be expressed through classical reach-avoid properties and show that risk-aware objectives improve the uncertainty reduction in a robot's belief.