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    ํ•™์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

    Risk-Sensitive Motion Planning using Entropic Value-at-Risk

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    We consider the problem of risk-sensitive motion planning in the presence of randomly moving obstacles. To this end, we adopt a model predictive control (MPC) scheme and pose the obstacle avoidance constraint in the MPC problem as a distributionally robust constraint with a KL divergence ambiguity set. This constraint is the dual representation of the Entropic Value-at-Risk (EVaR). Building upon this viewpoint, we propose an algorithm to follow waypoints and discuss its feasibility and completion in finite time. We compare the policies obtained using EVaR with those obtained using another common coherent risk measure, Conditional Value-at-Risk (CVaR), via numerical experiments for a 2D system. We also implement the waypoint following algorithm on a 3D quadcopter simulation

    Distributionally Robust Model Predictive Control with Total Variation Distance

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    This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. The distributionally robust chance constraint is over-approximated as a tightened chance constraint, wherein the tightening for each time step in the MPC can be computed offline, hence reducing the computational burden. We conclude with numerical experiments to support our results on the probabilistic guarantees and computational efficiency

    Risk-Averse Receding Horizon Motion Planning

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    This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.Comment: Submitted to Artificial Intelligence Journal, Special Issue on Risk-aware Autonomous Systems: Theory and Practice. arXiv admin note: text overlap with arXiv:2011.1121
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