177 research outputs found
Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming
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
ํ์ต ๊ธฐ๋ฐ ์์จ์์คํ ์ ๋ฆฌ์คํฌ๋ฅผ ๊ณ ๋ คํ๋ ๋ถํฌ์ ๊ฐ์ธ ์ต์ ํ
ํ์๋
ผ๋ฌธ (์์ฌ) -- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ์ ๊ธฐยท์ ๋ณด๊ณตํ๋ถ, 2020. 8. ์์ธ์.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 ์ฐ๊ตฌ์์ ์์จ ์์คํ
์ด ์๋ ค์ง์ง ์์ ํ๋ฅ ๋ถํฌ๋ก ๋๋คํ๊ฒ ์์ง์ด๋ ์ฅ์ ๋ฌผ์ ํผํ๊ธฐ ์ํ ์ํ ์ธ์์ ๊ณ ๋ คํ๋ ๋ชจ์
์ ์ด ๊ธฐ๋ฒ์ ๊ฐ๋ฐํ๋ค. ๋ฐ๋ผ์ ๋ณธ ๋
ผ๋ฌธ์์ ์์ ์ฑ๊ณผ ๋ณด์์ฑ์ ์ฒด๊ณ์ ์ผ๋ก ์กฐ์ ํ๋ ์๋ก์ด Model Predictive Control (MPC) ๋ฐฉ๋ฒ์ ์ ์ํ๋ค. ๋ณธ ๋ฐฉ๋ฒ์ ํต์ฌ ์์๋ MPC ๋ฌธ์ ์ ์์ ์ฑ ๋ฆฌ์คํฌ๋ฅผ ์ ํํ๋ Conditional Value-at-Risk (CVaR)๋ผ๋ ๋ฆฌ์คํฌ ์ฒ๋์ด๋ค. ์์ ์ฑ ๋ฆฌ์คํฌ๋ฅผ ๊ณ์ฐํ๊ธฐ ์ํด ์ ํ๋ ์์ ํ๋ณธ ๋ฐ์ดํฐ๋ฅผ ์ด์ฉํ์ฌ ์ป์ด์ง ๊ฒฝํ์ ๋ถํฌ๋ฅผ ์ฌ์ฉํ๋ Sample Average Approximation (SAA)์ ์ ์ฉํ๋ค.
๋ํ, ๊ฒฝํ์ ๋ถํฌ๋ก๋ถํฐ ์ค์ ๋ถํฌ๊ฐ Ambiguity Set๋ผ๋ ์งํฉ ๋ด์์ ๋ฒ์ด๋๋ ๋ฆฌ์คํฌ๋ฅผ ์ ํํ๋ ๋ฐฉ๋ฒ์ ์ ์ํ๋ค.
Ambiguity Set๋ฅผ Wasserstein ๊ฑฐ๋ฆฌ๋ก ์ธก์ ๋ ๋ฐ์ง๋ฆ์ ๊ฐ์ง ํต๊ณ์ ๊ณต์ผ๋ก ์ ํํจ์ผ๋ก์จ ํ๋ จ ๋ฐ์ดํฐ์ ๋
๋ฆฝ์ ์ผ๋ก ์์ฑ๋ ์๋ก์ด ์ํ ๋ฐ์ดํฐ๋ฅผ ์ฌ์ฉํ์ฌ ํ๊ฐํ out-of-sample risk์ ๋ํ ํ๋ฅ ์ ๋ณด์ฅ์ ๋ฌ์ฑํ๋ค.
๋ณธ ๋
ผ๋ฌธ์์ SAA๊ธฐ๋ฐ MPC (SAA-MPC)์ Wasserstein Distributionally Robust MPC (DR-MPC)๋ฅผ ์ฌ๋ฌ ๊ณผ์ ์ ํตํ์ฌ ๋ค๋ฃจ๊ธฐ ์ฌ์ด ํ๋ก๊ทธ๋จ์ผ๋ก ์ฌํธ์ฑํ๋ค.
๋ํ, ํ๊ฒฝ์ ๊ณผ๊ฑฐ ๊ด์ธก์ผ๋ก๋ถํฐ ์ฅ์ ๋ฌผ์ ๋ฏธ๋ ์์ง์์ ์์ธกํ๊ธฐ ์ํด Distributionally Robust MPC ๋ฐฉ๋ฒ์ Gaussian Process (GP)์ ๊ฒฐํฉํ๋ค. ๋ณธ ์ฐ๊ตฌ์์ ๊ฐ๋ฐ๋๋ ๊ธฐ๋ฒ๋ค์ ์ฑ๋ฅ์ ๋น์ ํ ์๋์ฐจ ๋ชจ๋ธ๊ณผ ์ ํํ๋ ์ฟผ๋๋กํฐ ๋ชจ๋ธ์ ์ด์ฉํ ์๋ฎฌ๋ ์ด์
์ฐ๊ตฌ๋ฅผ ํตํ์ฌ ๋ถ์ํ๋ค.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
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
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
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
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
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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