Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

A primal-dual flow for affine constrained convex optimization

We introduce a novel primal-dual flow for affine constrained convex optimization problem. As a modification of the standard saddle-point system, our primal-dual flow is proved to possesses the exponential decay property, in terms of a tailored Lyapunov function. Then a class of primal-dual methods for the original optimization problem are obtained from numerical discretizations of the continuous flow, and with a unified discrete Lyapunov function, nonergodic convergence rates are established. Among those algorithms, we can recover the (linearized) augmented Lagrangian method and the quadratic penalty method with continuation technique. Also, new methods with a special inner problem, that is a linear symmetric positive definite system or a nonlinear equation which may be solved efficiently via the semi-smooth Newton method, have been proposed as well. Especially, numerical tests on the linearly constrained $l_1$-$l_2$ minimization show that our method outperforms the accelerated linearized Bregman method

An approximate model for optimizing Bernoulli columns against buckling

International audienceProposed herein is a simple but powerful method for optimization of inhomogeneous, elastically restrained columns against buckling when subjected to both compressive concentrated and distributed axial loads that include self-weight. Unlike previously published studies on the subject, we do not have to specify any prescribed geometrical variation and analysis may be readily performed on columns with any complex geometrical shape. In the proposed method, the differential equation governing the buckling of Euler columns is discretized by adopting the Hencky bar-chain model, and critical buckling loads are evaluated by seeking the lowest eigenvalue of the resulting system of algebraic equations. The discrete nature of the formulation, as well as the reduced number of parameters to be optimized, is well suited for the adopted optimization process that is based on evolutionary algorithms. We propose an optimization scheme based on a parallel genetic algorithm. A comparisori study between the obtained optimal column shape and buckling loads on homogeneous and isotropic columns with circular cross section, and the numerical and analytical solutions found in the open literature shows fast convergence, high accuracy and flexibility of the proposed method