Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Ahmadi, Mohamadreza; Xiong, Xiaobin; Ames, Aaron D.

doi:10.1109/lcsys.2021.3086854

Cited by 33 publications

(15 citation statements)

References 30 publications

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“…Value-at-Risk: Value-at-Risk (VaR) is a statistic used quite frequently in the financial literature to determine an individual's exposure to risk [18], [19]. Both VaR and other risk measures have also been used quite frequently in the controls literature to determine safe actions in a worst-case sense [9], [20], [21]. Succinctly though, VaR is defined as follows.…”

Section: A Preliminaries and Problem Formulationmentioning

confidence: 99%

A Scenario Approach to Risk-Aware Safety-Critical System Verification

Akella¹,

Ahmadi²,

Ames³

2022

Preprint

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With the growing interest in deploying robots in unstructured and uncertain environments, there has been increasing interest in factoring risk into safety-critical control development. Similarly, the authors believe risk should also be accounted in the verification of these controllers. In pursuit of sample-efficient methods for uncertain black-box verification then, we first detail a method to estimate the Value-at-Risk of arbitrary scalar random variables without requiring apriori knowledge of its distribution. Then, we reformulate the uncertain verification problem as a Value-at-Risk estimation problem making use of our prior results. In doing so, we provide fundamental sampling requirements to bound with high confidence the volume of states and parameters for a blackbox system that could potentially yield unsafe phenomena. We also show that this procedure works independent of system complexity through simulated examples of the Robotarium.

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Section: A Preliminaries and Problem Formulationmentioning

confidence: 99%

A Scenario Approach to Risk-Aware Safety-Critical System Verification

Akella¹,

Ahmadi²,

Ames³

2022

Preprint

Self Cite

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“…Risk-aware model predictive control was considered in [29,76], while [17,73] present data-driven and distributionally robust model predictive controllers. Risk-aware control barrier functions for safe control synthesis were proposed in [2], while [58] demonstrates the use of risk in sampling-based planning. We remark that we view these works to be orthogonal to our paper as we provide a data-driven framework for the risk assessment under complex temporal logic specifications, and we hope to inform future control design strategies.…”

Section: Related Workmentioning

confidence: 99%

“…1 We use the notation 𝔉 (𝐴, 𝐵) to denote the set of all measurable functions mapping from the domain 𝐴 into the domain 𝐵, i.e., an element 𝑓 ∈ 𝔉(𝐴, 𝐵) is a measurable function 𝑓 : 𝐴 → 𝐵. 2 We use the notation ⊕ and ⊖ to denote the Minkowski sum and the Minkowski difference, respectively. where R := R ∪ {−∞, ∞} is the set of extended real numbers and where 𝑑 : R 𝑛 × R 𝑛 → R is a metric assigning a distance in R 𝑛 , e.g., the Euclidean norm.…”

Section: Signal Temporal Logicmentioning

confidence: 99%

Risk of Stochastic Systems for Temporal Logic Specifications

Lindemann¹,

Jiang²,

Matni³

et al. 2022

Preprint

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Fig. 1. Left: Simulation environment in the autonomous driving simulator CARLA. Middle: Double left turn on which we evaluate four trained neural network lane keeping controllers. Right: Cross-track error 𝑐 𝑒 and orientation error 𝜃 𝑒 used for risk verification of the neural network controllers.The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful demonstrations of these technologies, critical system failures have repeatedly been reported. Even if rare, such system failures pose a serious barrier to adoption without a rigorous risk assessment. This paper presents a framework for the systematic and rigorous risk verification of systems. We consider a wide range of system specifications formulated in signal temporal logic (STL) and model the system as a stochastic process, permitting discrete-time and continuous-time stochastic processes. We then define the STL robustness risk as the risk of lacking robustness against failure. This definition is motivated as system failures are often caused by missing robustness to modeling errors, system disturbances, and distribution shifts in the underlying data generating process. Within the definition, we permit general classes of risk measures and focus on tail risk measures such as the value-at-risk and the conditional value-at-risk. While the STL robustness risk is in general hard to compute, we propose the approximate STL robustness risk as a more tractable notion that upper bounds the STL robustness risk. We show how the approximate STL robustness risk can accurately be estimated from system trajectory data. For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly. We illustrate our verification algorithm in the autonomous driving simulator CARLA and show how a least risky controller can be selected among four neural network lane keeping controllers for five meaningful system specifications.

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“…1) Global Position Control: The H-LIP based stepping can also be used for controlling the global position [61] of the underactuated bipedal robot [62], [63] by including the global position in the S2S dynamics. Then the H-LIP stepping can be used to approximately control the global position of the robot, where the feedback is on the error in terms of the global horizontal position, local horizontal position (w.r.t.…”

Section: Extensions and Future Directionsmentioning

confidence: 99%

3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization

Xiong¹,

Ames²

2021

Preprint

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In this paper, we present a Hybrid-Linear Inverted Pendulum (H-LIP) based approach for synthesizing and stabilizing 3D underactuated bipedal walking. The H-LIP model is proposed to capture the essential components of the underactuated part and actuated part of the robotic walking. The walking gait of the robot is then synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive their stepping stabilization. The step-to-step (S2S) dynamics of the H-LIP is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass (COM) of the robotic walking, which results in a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is evaluated in both simulation and experiment on the 3D underactuated bipedal robot Cassie, which demonstrate dynamic walking behaviors with both versatility and robustness.

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Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Cited by 33 publications

References 30 publications

A Scenario Approach to Risk-Aware Safety-Critical System Verification

A Scenario Approach to Risk-Aware Safety-Critical System Verification

Risk of Stochastic Systems for Temporal Logic Specifications

3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization

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