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The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
Despite recent advancements in 3D-text cross-modal alignment, existing state-of-the-art methods still struggle to align fine-grained textual semantics with detailed geometric structures, and their alignment performance degrades…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
Aircraft failures alter dynamics, diminishing manoeuvrability. Such manoeuvring flight envelope variations, governed by the aircraft's complex nonlinear dynamics, are unpredictable by pilots and existing flight management systems. To…
Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…
Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…
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…
A numerical method ADER-DG with a local DG predictor for solving a DAE system has been developed, which was based on the formulation of ADER-DG methods using a local DG predictor for solving ODE and PDE systems. The basis functions were…
Generalized Polynomial Chaos (gPC) theory has been widely used for representing parametric uncertainty in a system, thanks to its ability to propagate uncertainty evolution. In an optimal control context, gPC can be combined with several…
We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…
We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and…
The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while…
To generate reliable motion for legged robots through trajectory optimization, it is crucial to simultaneously compute the robot's path and contact sequence, as well as accurately consider the dynamics in the problem formulation. In this…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations.…
Most mobile robots follow a modular sense-planact system architecture that can lead to poor performance or even catastrophic failure for visual inertial navigation systems due to trajectories devoid of feature matches. Planning in belief…