Related papers: Dimensionally Homogeneous Jacobian using Extended …
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice with Laplacian and potential terms modulated by a primitive invertible two-letter substitution. We investigate the spectrum and the spectral type, the…
Differential drive mobile manipulators combine the mobility of wheeled bases with the manipulation capability of multi-joint arms, enabling versatile applications but posing considerable challenges for trajectory planning due to their…
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization…
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…
To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space…
Vehicle platooning has been shown to be quite fruitful in the transportation industry to enhance fuel economy, road throughput, and driving comfort. Model Predictive Control (MPC) is widely used in literature for platoon control to achieve…
In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…
Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in…
The subject of this paper is the optimal design of a parallel mechanism intended for three-axis machining applications. Parallel mechanisms are interesting alternative designs in this context but most of them are designed for three- or…
In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm…
In this paper we present a new approach for dynamic motion planning for legged robots. We formulate a trajectory optimization problem based on a compact form of the robot dynamics. Such a form is obtained by projecting the rigid body…
We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…