Related papers: Constrained Trajectory Optimization on Matrix Lie …
We present an algorithm for obtaining an optimal control policy for hybrid dynamical systems in cluttered environments. To the best of our knowledge, this is the first attempt to have a locally optimal solution for this specific problem…
Distributed trajectory optimization via ADMM-DDP is a powerful approach for coordinating multi-agent systems, but it requires extensive tuning of tightly coupled hyperparameters that jointly govern local task performance and global…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
Learning-based motion planning can quickly generate near-optimal trajectories. However, it often requires either large training datasets or costly collection of human demonstrations. This work proposes an alternative approach that quickly…
This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…
In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…
We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…
The configuration of most robotic systems lies in continuous transformation groups. However, in mobile robot trajectory tracking, many recent works still naively utilize optimization methods for elements in vector space without considering…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…
The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…