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A novel learning Model Predictive Control technique is applied to the autonomous racing problem. The goal of the controller is to minimize the time to complete a lap. The proposed control strategy uses the data from previous laps to improve…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
This paper is concerned with optimal power flow (OPF), which is the problem of optimizing the transmission of electricity in power systems. Our main contributions are as follows: (i) we propose a novel parabolic relaxation, which transforms…
In this paper we provide an optimal control based strategy to explore feasible trajectories of nonlinear systems, that is to find curves that satisfy the dynamics as well as point-wise state-input constraints. The strategy is interesting…
In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
In this paper, we consider nonconvex optimization problems with nonlinear equality constraints. We assume that the objective function and the functional constraints are locally smooth. To solve this problem, we introduce a linearized…
A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau-Yosida…
Nonlinear model predictive control (NMPC) is a popular strategy for solving motion planning problems, including obstacle avoidance constraints, in autonomous driving applications. Non-smooth obstacle shapes, such as rectangles, introduce…
This paper is based on a crucial issue in the aviation world: how to optimize the trajectory and controls given to the aircraft in order to optimize flight time and fuel consumption. This study aims to provide elements of a response to this…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
In this paper, we propose a new model predictive control (MPC) formulation for autonomous driving. The novelty of our MPC stems from the following results. Firstly, we adopt an alternating minimization approach wherein linear velocities and…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments cluttered with obstacles having arbitrary convex shapes. The proposed navigation approach relies on a hybrid feedback to guarantee global…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…