Related papers: Reliable Solution to Dynamic Optimization Problems…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
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…
Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have rarely been compared in terms of solution and speed. Through…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete…
This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized…
Distributionally robust optimization (DRO) is an effective framework for controlling real-world systems with various uncertainties, typically modeled using distributional uncertainty balls. However, DRO problems often involve infinitely…
This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control…
The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…
Decision and control are core functionalities of high-level automated vehicles. Current mainstream methods, such as functionality decomposition and end-to-end reinforcement learning (RL), either suffer high time complexity or poor…
Stochastic and (distributionally) robust optimization problems often become computationally challenging as the number of scenarios or data points increases. Scenario reduction is therefore a key technique for improving tractability. We…
We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank…