177 research outputs found

    Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming

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    Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to stochasticity and further distributional shift from the nominal one. In this paper, we present distributional robust CBF (DR-CBF) to achieve resilience under distributional shift while keeping the advantages of CBF, such as computational efficacy and forward invariance. To achieve this goal, we first propose a single-level convex reformulation to estimate the conditional value at risk (CVaR) of the safety constraints under distributional shift measured by a Wasserstein metric, which is by nature tri-level programming. Moreover, to construct a control barrier condition to enforce the forward invariance of the CVaR, the technique of differentiable convex programming is applied to enable differentiation through the optimization layer of CVaR estimation. We also provide an approximate variant of DR-CBF for higher-order systems. Simulation results are presented to validate the chance-constrained safety guarantee under the distributional shift in both first and second-order systems

    ํ•™์Šต ๊ธฐ๋ฐ˜ ์ž์œจ์‹œ์Šคํ…œ์˜ ๋ฆฌ์Šคํฌ๋ฅผ ๊ณ ๋ คํ•˜๋Š” ๋ถ„ํฌ์  ๊ฐ•์ธ ์ตœ์ ํ™”

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    ํ•™์œ„๋…ผ๋ฌธ (์„์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์ „๊ธฐยท์ •๋ณด๊ณตํ•™๋ถ€, 2020. 8. ์–‘์ธ์ˆœ.In this thesis, a risk-aware motion control scheme is considered for autonomous systems to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method for motion planning and decision-making that systematically adjusts the safety and conservativeness in an environment with randomly moving obstacles. The key component is the Conditional Value-at-Risk (CVaR), employed to limit the safety risk in the MPC problem. Having the empirical distribution obtained using a limited amount of sample data, Sample Average Approximation (SAA) is applied to compute the safety risk. Furthermore, we propose a method, which limits the risk of unsafety even when the true distribution of the obstacles movements deviates, within an ambiguity set, from the empirical one. By choosing the ambiguity set as a statistical ball with its radius measured by the Wasserstein metric, we achieve a probabilistic guarantee of the out-of-sample risk, evaluated using new sample data generated independently of the training data. A set of reformulations are applied on both SAA-based MPC (SAA-MPC) and Wasserstein Distributionally Robust MPC (DR-MPC) to make them tractable. In addition, we combine the DR-MPC method with Gaussian Process (GP) to predict the future motion of the obstacles from past observations of the environment. The performance of the proposed methods is demonstrated and analyzed through simulation studies using a nonlinear vehicle model and a linearized quadrotor model.๋ณธ ์—ฐ๊ตฌ์—์„œ ์ž์œจ ์‹œ์Šคํ…œ์ด ์•Œ๋ ค์ง€์ง€ ์•Š์€ ํ™•๋ฅ  ๋ถ„ํฌ๋กœ ๋žœ๋คํ•˜๊ฒŒ ์›€์ง์ด๋Š” ์žฅ์• ๋ฌผ์„ ํ”ผํ•˜๊ธฐ ์œ„ํ•œ ์œ„ํ—˜ ์ธ์‹์„ ๊ณ ๋ คํ•˜๋Š” ๋ชจ์…˜ ์ œ์–ด ๊ธฐ๋ฒ•์„ ๊ฐœ๋ฐœํ•œ๋‹ค. ๋”ฐ๋ผ์„œ ๋ณธ ๋…ผ๋ฌธ์—์„œ ์•ˆ์ „์„ฑ๊ณผ ๋ณด์ˆ˜์„ฑ์„ ์ฒด๊ณ„์ ์œผ๋กœ ์กฐ์ ˆํ•˜๋Š” ์ƒˆ๋กœ์šด Model Predictive Control (MPC) ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•œ๋‹ค. ๋ณธ ๋ฐฉ๋ฒ™์˜ ํ•ต์‹ฌ ์š”์†Œ๋Š” MPC ๋ฌธ์ œ์˜ ์•ˆ์ „์„ฑ ๋ฆฌ์Šคํฌ๋ฅผ ์ œํ•œํ•˜๋Š” Conditional Value-at-Risk (CVaR)๋ผ๋Š” ๋ฆฌ์Šคํฌ ์ฒ™๋„์ด๋‹ค. ์•ˆ์ „์„ฑ ๋ฆฌ์Šคํฌ๋ฅผ ๊ณ„์‚ฐํ•˜๊ธฐ ์œ„ํ•ด ์ œํ•œ๋œ ์–‘์˜ ํ‘œ๋ณธ ๋ฐ์ดํ„ฐ๋ฅผ ์ด์šฉํ•˜์—ฌ ์–ป์–ด์ง„ ๊ฒฝํ—˜์  ๋ถ„ํฌ๋ฅผ ์‚ฌ์šฉํ•˜๋Š” Sample Average Approximation (SAA)์„ ์ ์šฉํ•œ๋‹ค. ๋˜ํ•œ, ๊ฒฝํ—˜์  ๋ถ„ํฌ๋กœ๋ถ€ํ„ฐ ์‹ค์ œ ๋ถ„ํฌ๊ฐ€ Ambiguity Set๋ผ๋Š” ์ง‘ํ•ฉ ๋‚ด์—์„œ ๋ฒ—์–ด๋‚˜๋„ ๋ฆฌ์Šคํฌ๋ฅผ ์ œํ•œํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•œ๋‹ค. Ambiguity Set๋ฅผ Wasserstein ๊ฑฐ๋ฆฌ๋กœ ์ธก์ •๋œ ๋ฐ˜์ง€๋ฆ„์„ ๊ฐ€์ง„ ํ†ต๊ณ„์  ๊ณต์œผ๋กœ ์„ ํƒํ•จ์œผ๋กœ์จ ํ›ˆ๋ จ ๋ฐ์ดํ„ฐ์™€ ๋…๋ฆฝ์ ์œผ๋กœ ์ƒ์„ฑ๋œ ์ƒˆ๋กœ์šด ์ƒ˜ํ”Œ ๋ฐ์ดํ„ฐ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ํ‰๊ฐ€ํ•œ out-of-sample risk์— ๋Œ€ํ•œ ํ™•๋ฅ ์  ๋ณด์žฅ์„ ๋‹ฌ์„ฑํ•œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ SAA๊ธฐ๋ฐ˜ MPC (SAA-MPC)์™€ Wasserstein Distributionally Robust MPC (DR-MPC)๋ฅผ ์—ฌ๋Ÿฌ ๊ณผ์ •์„ ํ†ตํ•˜์—ฌ ๋‹ค๋ฃจ๊ธฐ ์‰ฌ์šด ํ”„๋กœ๊ทธ๋žจ์œผ๋กœ ์žฌํŽธ์„ฑํ•œ๋‹ค. ๋˜ํ•œ, ํ™˜๊ฒฝ์˜ ๊ณผ๊ฑฐ ๊ด€์ธก์œผ๋กœ๋ถ€ํ„ฐ ์žฅ์• ๋ฌผ์˜ ๋ฏธ๋ž˜ ์›€์ง์ž„์„ ์˜ˆ์ธกํ•˜๊ธฐ ์œ„ํ•ด Distributionally Robust MPC ๋ฐฉ๋ฒ•์„ Gaussian Process (GP)์™€ ๊ฒฐํ•ฉํ•œ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ ๊ฐœ๋ฐœ๋˜๋Š” ๊ธฐ๋ฒ•๋“ค์˜ ์„ฑ๋Šฅ์„ ๋น„์„ ํ˜• ์ž๋™์ฐจ ๋ชจ๋ธ๊ณผ ์„ ํ˜•ํ™”๋œ ์ฟผ๋“œ๋กœํ„ฐ ๋ชจ๋ธ์„ ์ด์šฉํ•œ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ์—ฐ๊ตฌ๋ฅผ ํ†ตํ•˜์—ฌ ๋ถ„์„ํ•œ๋‹ค.1 BACKGROUND AND OBJECTIVES 1 1.1 Motivation and Objectives 1 1.2 Research Contributions 2 1.3 Thesis Organization 3 2 RISK-AWARE MOTION PLANNING AND CONTROL USING CVAR-CONSTRAINED OPTIMIZATION 5 2.1 Introduction 5 2.2 System and Obstacle Models 8 2.3 CVaR-constrained Motion Planning and Control 10 2.3.1 Reference Trajectory Planning 10 2.3.2 Safety Risk 11 2.3.3 Risk-Constrained Model Predictive Control 13 2.3.4 Linearly Constrained Mixed Integer Convex Program 18 2.4 Numerical Experiments 20 2.4.1 Effect of Confidence Level 21 2.4.2 Effect of Sample Size 23 2.5 Conclusions 24 3 WASSERSTEIN DISTRIBUTIONALLY ROBUST MPC 28 3.1 Introduction 28 3.2 System and Obstacle Models 31 3.3 Wasserstein Distributionally Robust MPC 33 3.3.1 Distance to the Safe Region 36 3.3.2 Reformulation of Distributionally Robust Risk Constraint 38 3.3.3 Reformulation of the Wasserstein DR-MPC Problem 43 3.4 Out-of-Sample Performance Guarantee 45 3.5 Numerical Experiments 47 3.5.1 Nonlinear Car-Like Vehicle Model 48 3.5.2 Linearized Quadrotor Model 53 3.6 Conclusions 57 4 LEARNING-BASED DISTRIBUTIONALLY ROBUST MPC 58 4.1 Introduction 58 4.2 Learning the Movement of Obstacles Using Gaussian Processes 60 4.2.1 Obstacle Model 60 4.2.2 Gaussian Process Regression 61 4.2.3 Prediction of the Obstacle's Motion 63 4.3 Gaussian Process based Wasserstein DR-MPC 65 4.4 Numerical Experiments 70 4.5 Conclusions 74 5 CONCLUSIONS AND FUTURE WORK 75 Abstract (In Korean) 87Maste

    Fast Second-order Cone Programming for Safe Mission Planning

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    This paper considers the problem of safe mission planning of dynamic systems operating under uncertain environments. Much of the prior work on achieving robust and safe control requires solving second-order cone programs (SOCP). Unfortunately, existing general purpose SOCP methods are often infeasible for real-time robotic tasks due to high memory and computational requirements imposed by existing general optimization methods. The key contribution of this paper is a fast and memory-efficient algorithm for SOCP that would enable robust and safe mission planning on-board robots in real-time. Our algorithm does not have any external dependency, can efficiently utilize warm start provided in safe planning settings, and in fact leads to significant speed up over standard optimization packages (like SDPT3) for even standard SOCP problems. For example, for a standard quadrotor problem, our method leads to speedup of 1000x over SDPT3 without any deterioration in the solution quality. Our method is based on two insights: a) SOCPs can be interpreted as optimizing a function over a polytope with infinite sides, b) a linear function can be efficiently optimized over this polytope. We combine the above observations with a novel utilization of Wolfe's algorithm to obtain an efficient optimization method that can be easily implemented on small embedded devices. In addition to the above mentioned algorithm, we also design a two-level sensing method based on Gaussian Process for complex obstacles with non-linear boundaries such as a cylinder

    Decision-theoretic MPC: Motion Planning with Weighted Maneuver Preferences Under Uncertainty

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    Continuous optimization based motion planners require deciding on a maneuver homotopy before optimizing the trajectory. Under uncertainty, maneuver intentions of other participants can be unclear, and the vehicle might not be able to decide on the most suitable maneuver. This work introduces a method that incorporates multiple maneuver preferences in planning. It optimizes the trajectory by considering weighted maneuver preferences together with uncertainties ranging from perception to prediction while ensuring the feasibility of a chance-constrained fallback option. Evaluations in both driving experiments and simulation studies show enhanced interaction capabilities and comfort levels compared to conventional planners, which consider only a single maneuver

    Distributionally Consistent Simulation of Naturalistic Driving Environment for Autonomous Vehicle Testing

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    Microscopic traffic simulation provides a controllable, repeatable, and efficient testing environment for autonomous vehicles (AVs). To evaluate AVs' safety performance unbiasedly, ideally, the probability distributions of the joint state space of all vehicles in the simulated naturalistic driving environment (NDE) needs to be consistent with those from the real-world driving environment. However, although human driving behaviors have been extensively investigated in the transportation engineering field, most existing models were developed for traffic flow analysis without consideration of distributional consistency of driving behaviors, which may cause significant evaluation biasedness for AV testing. To fill this research gap, a distributionally consistent NDE modeling framework is proposed. Using large-scale naturalistic driving data, empirical distributions are obtained to construct the stochastic human driving behavior models under different conditions, which serve as the basic behavior models. To reduce the model errors caused by the limited data quantity and mitigate the error accumulation problem during the simulation, an optimization framework is designed to further enhance the basic models. Specifically, the vehicle state evolution is modeled as a Markov chain and its stationary distribution is twisted to match the distribution from the real-world driving environment. In the case study of highway driving environment using real-world naturalistic driving data, the distributional accuracy of the generated NDE is validated. The generated NDE is further utilized to test the safety performance of an AV model to validate its effectiveness.Comment: 32 pages, 9 figure

    Winning the 3rd Japan Automotive AI Challenge -- Autonomous Racing with the Autoware.Auto Open Source Software Stack

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    The 3rd Japan Automotive AI Challenge was an international online autonomous racing challenge where 164 teams competed in December 2021. This paper outlines the winning strategy to this competition, and the advantages and challenges of using the Autoware.Auto open source autonomous driving platform for multi-agent racing. Our winning approach includes a lane-switching opponent overtaking strategy, a global raceline optimization, and the integration of various tools from Autoware.Auto including a Model-Predictive Controller. We describe the use of perception, planning and control modules for high-speed racing applications and provide experience-based insights on working with Autoware.Auto. While our approach is a rule-based strategy that is suitable for non-interactive opponents, it provides a good reference and benchmark for learning-enabled approaches.Comment: Accepted at Autoware Workshop at IV 202

    Risk of Stochastic Systems for Temporal Logic Specifications

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    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

    Activity Report 2022

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