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This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
In this paper, we address the real-time risk-bounded safety verification problem of continuous-time state trajectories of autonomous systems in the presence of uncertain time-varying nonlinear safety constraints. Risk is defined as the…
Destination prediction is an essential task in a variety of mobile applications. In this paper, we optimize the matrix operation and adapt a semi-lazy framework to improve the prediction accuracy and efficiency of a state-of-the-art…
This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
Obstacle avoidance for multi-robot navigation with polytopic shapes is challenging. Existing works simplify the system dynamics or consider it as a convex or non-convex optimization problem with positive distance constraints between robots,…
We consider the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain locations. While previous approaches model the uncertainties with a prescribed Gaussian distribution, we consider the realistic…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
We report a globally-optimal approach to robotic path planning under uncertainty, based on the theory of quantitative measures of formal languages. A significant generalization to the language-measure-theoretic path planning algorithm…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…
The number of multi-robot systems deployed in field applications has increased dramatically over the years. Despite the recent advancement of navigation algorithms, autonomous robots often encounter challenging situations where the control…