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Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of…
The resurgence of lunar operations requires advancements in cislunar navigation and Space Situational Awareness (SSA). Challenges associated to these tasks have created an interest in autonomous planning, navigation, and tracking…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
This paper investigates the collaboration of multiple connected and automated vehicles (CAVs) in different scenarios. In general, the collaboration of CAVs can be formulated as a nonlinear and nonconvex model predictive control (MPC)…
Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
This paper addresses the problem of trajectory optimization for an unmanned surface vehicle while considering direction-dependent ocean currents and flexible refueling constraints. This work is motivated by the rising interest in developing…
We propose an online iterative algorithm to optimize a convex cover to under-approximate the free space for autonomous navigation to delineate Safe Flight Corridors (SFC). The convex cover consists of a set of polytopes such that the union…
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control…
Guidance and control (G&C) technologies play a central role in the development and operation of vehicular systems. The emergence of computational guidance and control (CG&C) and highly efficient numerical algorithms has opened up the great…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
Designing robust trajectories under uncertainties is an emerging technology that may represent a key paradigm shift in space mission design. As we pursue more ambitious scientific goals (e.g., multi-moon tours, missions with extensive…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…