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1. A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems

   Chapman, Margaret P.; Jonathan, Lacotte; Aviv, Tamar Donggun; Lee, Kevin M.; Jaime, F. Fisac; Jha, Susmit; Marco, Pavone; Claire, Tomlin (July 2019, AMERICAN CONTROL CONFERENCE)

   A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis). 

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2. A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems

   https://doi.org/10.23919/ACC.2019.8815169  

   Chapman, Margaret P.; Lacotte, Jonathan; Tamar, Aviv; Lee, Donggun; Smith, Kevin M.; Cheng, Victoria; Fisac, Jaime F.; Jha, Susmit; Pavone, Marco; Tomlin, Claire J. (July 2019, American Control Conference)

   A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis). 

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3. Integrated Task and Motion Planning for Safe Legged Navigation in Partially Observable Environments

   https://doi.org/10.1109/TRO.2023.3299524  

   Shamsah, Abdulaziz; Gu, Zhaoyuan; Warnke, Jonas; Hutchinson, Seth; Zhao, Ye (August 2023, IEEE Transactions on Robotics)

   This study proposes a hierarchically integrated framework for safe task and motion planning (TAMP) of bipedal locomotion in a partially observable environment with dynamic obstacles and uneven terrain. The high-level task planner employs linear temporal logic for a reactive game synthesis between the robot and its environment and provides a formal guarantee on navigation safety and task completion. To address environmental partial observability, a belief abstraction model is designed by partitioning the environment into multiple belief regions and employed at the high-level navigation planner to estimate the dynamic obstacles' location. This additional location information of dynamic obstacles offered by belief abstraction enables less conservative long-horizon navigation actions beyond guaranteeing immediate collision avoidance. Accordingly, a synthesized action planner sends a set of locomotion actions to the middle-level motion planner while incorporating safe locomotion specifications extracted from safety theorems based on a reduced-order model (ROM) of the locomotion process. The motion planner employs the ROM to design safety criteria and a sampling algorithm to generate nonperiodic motion plans that accurately track high-level actions. At the low level, a foot placement controller based on an angular-momentum linear inverted pendulum model is implemented and integrated with an ankle-actuated passivity-based controller for full-body trajectory tracking. To address external perturbations, this study also investigates the safe sequential composition of the keyframe locomotion state and achieves robust transitions against external perturbations through reachability analysis. The overall TAMP framework is validated with extensive simulations and hardware experiments on bipedal walking robots Cassie and Digit designed by Agility Robotics. 

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4. Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk

   https://doi.org/10.23919/ACC.2018.8430957  

   Samuelson, Samantha; Yang, Insoon (June 2018, 2018 Annual American Control Conference (ACC))

   In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set distance to formulate a safety risk-constrained optimal control problem. Our reformulation method using an extremal representation of the safety risk measure provides a computationally tractable dynamic programming solution. A useful byproduct of the proposed solution is the notion of a risk-constrained safe set, which is a new stochastic safety verification tool. We also establish useful connections between the risk-constrained safe sets and the popular probabilistic safe sets. The tradeoff between the risk tolerance and the mean performance of our controller is examined through an inventory control problem. 

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5. Safe Hierarchical Navigation in Crowded Dynamic Uncertain Environments

   https://doi.org/10.1109/CDC51059.2022.9992674  

   Chen, Hongyi; Feng, Shiyu; Zhao, Ye; Liu, Changliu; Vela, Patricio A. (December 2022, IEEE Conference on Decision and Control)

   This paper describes a hierarchical solution consisting of a multi-phase planner and a low-level safe controller to jointly solve the safe navigation problem in crowded, dynamic, and uncertain environments. The planner employs dynamic gap analysis and trajectory optimization to achieve collision avoidance with respect to the predicted trajectories of dynamic agents within the sensing and planning horizon and with robustness to agent uncertainty. To address uncertainty over the planning horizon and real-time safety, a fast reactive safe set algorithm (SSA) is adopted, which monitors and modifies the unsafe control during trajectory tracking. Compared to other existing methods, our approach offers theoretical guarantees of safety and achieves collision-free navigation with higher probability in uncertain environments, as demonstrated in scenarios with 20 and 50 dynamic agents. 

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