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1. Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis

   https://doi.org/10.1109/IROS45743.2020.9340755  

   Chou, Yi ; Yoon, Hansol ; Sankaranarayanan, Sriram ( October 2020 , 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   null (Ed.)

   We present a predictive runtime monitoring technique for estimating future vehicle positions and the probability of collisions with obstacles. Vehicle dynamics model how the position and velocity change over time as a function of external inputs. They are commonly described by discrete-time stochastic models. Whereas positions and velocities can be measured, the inputs (steering and throttle) are not directly measurable in these models. In our paper, we apply Bayesian inference techniques for real-time estimation, given prior distribution over the unknowns and noisy state measurements. Next, we pre-compute the set-valued reachability analysis to approximate future positions of a vehicle. The pre-computed reachability sets are combined with the posterior probabilities computed through Bayesian estimation to provided a predictive verification framework that can be used to detect impending collisions with obstacles. Our approach is evaluated using the coordinated-turn vehicle model for a UAV using on-board measurement data obtained from a flight test of a Talon UAV. We also compare the results with sampling-based approaches. We find that precomputed reachability analysis can provide accurate warnings up to 6 seconds in advance and the accuracy of the warnings improve as the time horizon is narrowed from 6 to 2 seconds. The approach also outperforms sampling in terms of on-board computation cost and accuracy measures. 

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2. Guaranteed Safe Path and Trajectory Tracking via Reachability Analysis Using Differential Inequalities

   Yang, Xuejiao ; Mu, Bowen ; Robertson, Dillard ; Scott, Joseph K. ( January 2023 , Journal of intelligent robotic systems)

   In many automated motion planning systems, vehicles are tasked with tracking a reference path or trajectory that is safe by design. However, due to various uncertainties, real vehicles may deviate from such references, potentially leading to collisions. This paper presents rigorous reachable set bounding methods for rapidly enclosing the set of possible deviations under uncertainty, which is critical information for online safety verification. The proposed approach applies recent advances in the theory of differential inequalities that exploit redundant model equations to achieve sharp bounds using only simple interval calculations. These methods have been shown to produce very sharp bounds at low cost for nonlinear systems in other application domains, but they rely on problem-specific insights to identify appropriate redundant equations, which makes them difficult to generalize and automate. Here, we demonstrate the application of these methods to tracking problems for the first time using three representative case studies. We find that defining redundant equations in terms of Lyapunov-like functions is particularly effective. The results show that this technique can produce effective bounds with computational times that are orders of magnitude less than the planned time horizon, making this a promising approach for online safety verification. This performance, however, comes at the cost of low generalizability, specifically due to the need for problem-specific insights and advantageous problem structure, such as the existence of appropriate Lyapunov-like functions. 

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3. Online predictive connected nd automated eco-driving on signalized arterials considering traffic control devices and road geometry constraints under uncertain traffic conditions

   https://doi.org/https://doi.org/10.1016/j.trb.2020.12.009  

   Zhao, S ; Zhang, K. ( March 2021 , Transportation research)

   null (Ed.)

   For energy-efficient Connected and Automated Vehicle (CAV) Eco-driving control on signalized arterials under uncertain traffic conditions, this paper explicitly considers traffic control devices (e.g., road markings, traffic signs, and traffic signals) and road geometry (e.g., road shapes, road boundaries, and road grades) constraints in a data-driven optimization-based Model Predictive Control (MPC) modeling framework. This modeling framework uses real-time vehicle driving and traffic signal data via Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) communications. In the MPC-based control model, this paper mathematically formulates location-based traffic control devices and road geometry constraints using the geographic information from High-Definition (HD) maps. The location-based traffic control devices and road geometry constraints have the potential to improve the safety, energy, efficiency, driving comfort, and robustness of connected and automated driving on real roads by considering interrupted flow facility locations and road geometry in the formulation. We predict a set of uncertain driving states for the preceding vehicles through an online learning-based driving dynamics prediction model. We then solve a constrained finite-horizon optimal control problem with the predicted driving states to obtain a set of Eco-driving references for the controlled vehicle. To obtain the optimal acceleration or deceleration commands for the controlled vehicle with the set of Eco-driving references, we formulate a Distributionally Robust Stochastic Optimization (DRSO) model (i.e., a special case of data-driven optimization models under moment bounds) with Distributionally Robust Chance Constraints (DRCC) with location-based traffic control devices and road geometry constraints. We design experiments to demonstrate the proposed model under different traffic conditions using real-world connected vehicle trajectory data and Signal Phasing and Timing (SPaT) data on a coordinated arterial with six actuated intersections on Fuller Road in Ann Arbor, Michigan from the Safety Pilot Model Deployment (SPMD) project. 

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4. Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

   https://doi.org/https://doi.org/10.1007/978-3-030-32430-8_23  

   Ramasubramanian, B ; Niu, L. ; Clark, A ; Bushnell, L ; Poovendran, R ( January 2019 , IEEE Conference on Decision and Game Theory for Security)

   This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discretetime dynamics. The temporal logic specification is given in safe−LTLF , a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zerosum discrete-time dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a safe − LTLF formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach. 

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5. 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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