Risk-Aware Autonomy Under Uncertainty

Nonlinear Probabilistic Planning, Control, Optimization, Estimation, and Learning Under Uncertainty for Autonomous Systems

Ashkan Jasour     

                                                                                                                                                                              © Ashkan Jasour, Last modified 2023-12.


1. Introduction:

Objective: This ongoing research aims to develop safe planning, control, and estimation algorithms for autonomous systems that account for uncertainties and nonlinear models and reason about probability of failure and success to ensure safety.


Probabilistic location of robot and unsafe area. Risk-aware algorithms reason about uncertainties and probability of failure and success. 
Acceptable risk level impacts the safety and optimality of the plan (trade-off between optimality and safety).


Existing Methods: Existing planning under uncertainty methods mainly fall into the following categories: i) Robust methods that work with worst-case planning scenarios and usually result in conservative plans,  ii) Probabilistic methods that rely on simplified uncertainty characterization and risk models, e.g., Gaussian linear models, that introduce another source of uncertainty not captured by the planner, and iii) Sampling-based methods that are known to be computationally expensive.


[Left: Sampling-based representation of uncertainties] Sampling-based methods use a large number of uncertainty samples in the planning process; Hence, they are computationally expensive and cannot guarantee the safety of the original uncertain system. [Middle: Gaussian approximation of uncertainties] Gaussian linear methods use linearized models and Gaussian approximation of the uncertainties and therefore they cannot guarantee the safety of the original uncertain system. [Right: Non-Gaussian uncertainties] We use nonlinear stochastic models where uncertainties are not necessarily Gaussian and generate plans with guaranteed bounded risk.


Challenges: 1) We need to deal with probabilistic/stochastic models and constraints,  2) Due to nonlinearities, probability distributions evolve into non-Gaussian distributions

Approach: To address planning under uncertainty problems: 1) We first formulate the planning under uncertainty problem as a probabilistic nonlinear planning problem with stochastic nonlinear models and probabilistic constraints on random variables, 2) We use higher-order moments to represent non-Gaussian probability distributions, 3) We transform stochastic models and probabilistic constraints on random variables into a set of deterministic models and constraints on the moments of probability distributions, 4) Finally, we solve the resulting deterministic optimization problem using off-the-shelf solvers. 









2. Mathematical Tools

4. Risk-Aware Safety Verification

5. Risk-Aware Planning

6. Risk-Aware Control

7. Risk-Aware Optimization