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Ensuring safety and driving consistency is a significant challenge for autonomous vehicles operating in partially observed environments. This work introduces a consistent parallel trajectory optimization (CPTO) approach to enable safe and…
This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ…
We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
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…
This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the…
Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate…
This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost,…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
The Online Bin Packing Problem (OBPP) is a sequential decision-making task in which each item must be placed immediately upon arrival, with no knowledge of future arrivals. Although recent deep-reinforcement-learning methods achieve…
Simultaneous Localization and Planning (SLAP) under process and measurement uncertainties is a challenge. It involves solving a stochastic control problem modeled as a Partially Observed Markov Decision Process (POMDP) in a general…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
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…
Motivated by the requirements for effectiveness and efficiency, path-speed decomposition-based trajectory planning methods have widely been adopted for autonomous driving applications. While a global route can be pre-computed offline,…