There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

United States. Department of Energy. Computational Science Graduate Fellowship Program (grant number DE-FG02-97ER25308)

Polyhedral approximation in mixed-integer convex optimization

In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method for limiting the risk of unsafety even when the true distribution of the obstacles' movements deviates, within an ambiguity set, from the empirical distribution obtained using a limited amount of sample data. 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. To resolve the infinite-dimensionality issue inherent in the distributionally robust MPC problem, we reformulate it as a finite-dimensional nonlinear program using modern distributionally robust optimization techniques based on the Kantorovich duality principle. To find a globally optimal solution in the case of affine dynamics and output equations, a spatial branch-and-bound algorithm is designed using McCormick relaxation. The performance of the proposed method is demonstrated and analyzed through simulation studies using a nonlinear car-like vehicle model and a linearized quadrotor model.

Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk

In the manufacturing industry, the smart factory is considered the final stage of the Fourth Industrial Revolution. Manufacturing companies are pursuing breakthroughs by introducing various advanced technologies to ensure their competitiveness. However, it is difficult for small and medium-sized enterprises (SMEs) to adopt smart-factory technologies, owing to financial and technical burdens. This paper proposes a smart factory that can be applied technically and strategically to the introduction of a smart factory for SMEs. The concept of an ‘appropriate smart factory’ involves applying appropriate measures in terms of cost and scale with consideration of the situations faced by SMEs. The goal is to build a smart factory that has necessary functions (Essential) but can be easily operated (Simple) at a low cost (Affordable) and has compatibility (Interoperable). This paper presents technical application measures such as appropriate smart sensors, appropriate IoT (Internet of Things), and small data processing, along with the definition of an appropriate smart factory. In addition, a case study was examined where the quality inspection equipment for garment manufacturing SMEs was developed by applying the appropriate smart factory concept.

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Appropriate Smart Factory for SMEs: Concept, Application and Perspective

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.

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

We propose a risk-aware motion planning and decision-making method that systematically adjusts the safety and conservativeness in an environment with randomly moving obstacles. The key component of this method is the conditional value-at-risk (CVaR) used to measure the safety risk that a robot faces. Unlike chance constraints, CVaR constraints are coherent, convex, and distinguish between tail events. We propose a two-stage method for safe motion planning and control: A reference trajectory is generated by using RRT* in the first stage, and then a receding horizon controller is employed to limit the safety risk by using CVaR constraints in the second stage. However, the second stage problem is nontrivial to solve, as it is a triple-level stochastic program. We develop a computationally tractable approach through 1) a reformulation of the CVaR constraints; 2) a sample average approximation; and 3) a linearly constrained mixed integer convex program formulation. The performance and utility of this risk-aware method are demonstrated via simulation using a 12-dimensional model of quadrotors.

Risk-Aware Motion Planning and Control Using CVaR-Constrained Optimization

In this paper, we propose an optimization-based decision-making tool for safe motion planning and control in an environment with randomly moving obstacles. The unique feature of the proposed method is that it limits the risk of unsafety by a pre-specified threshold even when the true probability distribution of the obstacles’ movements deviates, within a Wasserstein ball, from an available empirical distribution. Another advantage is that it provides a probabilistic out-of-sample performance guarantee of the risk constraint. To develop a computationally tractable method for solving the distributionally robust model predictive control problem, we propose a set of reformulation procedures using (i) the Kantorovich duality principle, (ii) the extremal representation of conditional value-at-risk, and (iii) a geometric expression of the distance to the union of halfspaces. The performance and utility of this distributionally robust method are demonstrated through simulations using a 12D quadrotor model in a 3D environment.

Wasserstein Distributionally Robust Motion Planning and Control with Safety Constraints Using Conditional Value-at-Risk

Safety is a critical issue in learning-based robotic and autonomous systems as learned information about their environments is often unreliable and inaccurate. In this paper, we propose a risk-aware motion control tool that is robust against errors in learned distributional information about obstacles moving with unknown dynamics. The salient feature of our model predictive control (MPC) method is its capability of limiting the risk of unsafety even when the true distribution deviates from the distribution estimated by Gaussian process (GP) regression, within an ambiguity set. Unfortunately, the distributionally robust MPC problem with GP is intractable because the worst-case risk constraint involves an infinite-dimensional optimization problem over the ambiguity set. To remove the infinite-dimensionality issue, we develop a systematic reformulation approach exploiting modern distributionally robust optimization techniques. The performance and utility of our method are demonstrated through simulations using a nonlinear car-like vehicle model for autonomous driving.

Astghik Hakobyan

Papers

Risk-Aware Motion Planning and Control Using CVaR-Constrained Optimization

Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk

Wasserstein Distributionally Robust Motion Planning and Control with Safety Constraints Using Conditional Value-at-Risk

Learning-Based Distributionally Robust Motion Control with Gaussian Processes

Learning-based distributionally robust motion control with Gaussian processes