Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formulating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.

Quadratic programming (QP) has become a core modelling component in the modern engineering toolkit. This is particularly true for simulation, planning and control in robotics. Yet, modern numerical solvers have not reached the level of efficiency and reliability required in practical applications where speed, robustness, and accuracy are all necessary. In this work, we introduce a few variations of the well-established augmented Lagrangian method, specifically for solving QPs, which include heuristics for improving practical numerical performances. Those variants are embedded within an open-source software which includes an efficient C++ implementation, a modular API, as well as best-performing heuristics for our test-bed. Relying on this framework, we present a benchmark studying the practical performances of modern optimization solvers for convex QPs on generic and complex problems of the literature as well as on common robotic scenarios. This benchmark notably highlights that this approach outperforms modern solvers in terms of efficiency, accuracy and robustness for small to medium-sized problems, while remaining competitive for higher dimensions.

In spite of the extensive media coverage of election technologies, the market and its players remain largely unknown. Who are they? What do they do? What are their strategies? This chapter leverages new empirical data to answer these questions, drawing in particular from a series of interviews with providers of political technology in France. We show that the sector is heterogeneous and that its boundaries are fluid, including actors who provide wildly different services and initially embraced different economic and technological strategies. We also show that the nature of the services provided as well as the partisan dimension of each company depends on its target customers. However, due to economic constraints, the sector is undergoing a radical restructuring. The laborious implementation of “elections 2.0” in France is continuing with an increasing professionalization of its players, leading the sector to become more homogeneous and internationalized.

Malgré la forte médiatisation des technologies au service des élections, ce marché et ses acteurs restent méconnus. Qui sont-ils ? Que font-ils ? Quelles sont leurs stratégies ? Pour répondre à ce manque, l’article apporte des connaissances empiriques nouvelles, notamment grâce à une série d’entretiens avec les acteurs de la technologie politique présents en France (LMP, NationBuilder, etc.). Contrairement au sens commun, nous montrons l’existence d’un groupe hétérogène, aux contours peu établis, dont les activités sont hétéroclites et dépendent de stratégies technologiques et économiques initialement distinctes. Nous montrons également que les services proposés et la dimension partisane des sociétés dépendent de la clientèle visée. Toutefois, en raison de contraintes économiques, le secteur connaît une profonde restructuration. La conquête difficile des élections 2.0 en France se poursuit avec une professionnalisation renforcée de ses acteurs, facteur d’une homogénéisation globale et internationalisée des acteurs.