When a human and a humanoid robot collaborate physically, ergonomics is a key factor to consider. Assuming a given humanoid robot, several control architectures exist nowadays to address ergonomic physical human-robot collaboration. This paper takes one step further by considering robot hardware parameters as optimization variables in the problem of collaborative payload lifting. The variables that parametrize robot's kinematics and dynamics ensure their physical consistency, and the human model is considered in the optimization problem. By leveraging the proposed modelling framework, the ergonomy of the interaction is maximized, here given by the agents' energy expenditure. Robot kinematic, dynamics, hardware constraints and human geometries are considered when solving the associated optimization problem. The proposed methodology is used to identify optimum hardware parameters for the design of the ergoCub robot, a humanoid possessing a degree of embodied intelligence for ergonomic interaction with humans. For the optimization problem, the starting point is the iCub humanoid robot. The obtained robot design reaches loads at heights in the range of 0.8-1.5 m with respect to the iCub robot whose range is limited to 0.8-1.2 m. The robot energy expenditure is decreased by about 33%, meanwhile, the human ergonomy is preserved, leading overall to an improved interaction.

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking, and have no obvious organization. But humans often look ahead when they walk, and could potentially plan anticipatory fluctuations for the terrain. Such planning is only sensible if it serves some an objective purpose, such as maintaining constant speed or reducing energy expenditure, that is also attainable within finite planning capacity. Here we show that humans do plan and perform optimal control strategies on uneven terrain. Rather than maintain constant speed, they make purposeful, anticipatory speed adjustments that are consistent with minimizing energy expenditure. A simple optimal control model predicts economical speed fluctuations that agree well with experiments with humans (N = 12) walking on seven different terrain profiles (correlated with model ro=0.55+-0.11, P<0.05 all terrains). Participants made repeatable speed fluctuations starting about six to eight steps ahead of each terrain feature (up to +-7.5 cm height difference each step, up to 16 consecutive features). Nearer features matter more, because energy is dissipated with each succeeding step collision with ground, preventing momentum from persisting indefinitely. A finite horizon of continuous look ahead and motor working space thus suffice to practically optimize for any length of terrain. Humans reason about walking in the near future to plan complex optimal control sequences.

Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be certified. Although such global optimality certificates have been well established for 3D \textit{pose-graph optimization}, the details have yet to be worked out for the 3D landmark-based SLAM problem, in which estimated states include both robot poses and map landmarks. In this paper, we address this gap by using a graph-theoretic approach to cast the subproblems of landmark-based SLAM into a form that yields a sufficient condition for global optimality. Efficient methods of computing the optimality certificates for these subproblems exist, but first require the construction of a large data matrix. We show that this matrix can be constructed with complexity that remains linear in the number of landmarks and does not exceed the state-of-the-art computational complexity of one local solver iteration. We demonstrate the efficacy of the certificate on simulated and real-world landmark-based SLAM problems. We also integrate our method into the state-of-the-art SE-Sync pipeline to efficiently solve landmark-based SLAM problems to global optimality. Finally, we study the robustness of the global optimality certificate to measurement noise, taking into consideration the effect of the underlying measurement graph.

We study the problem of imitating object interactions from Internet videos. This requires understanding the hand-object interactions in 4D, spatially in 3D and over time, which is challenging due to mutual hand-object occlusions. In this paper we make two main contributions: (1) a novel reconstruction technique RHOV (Reconstructing Hands and Objects from Videos), which reconstructs 4D trajectories of both the hand and the object using 2D image cues and temporal smoothness constraints; (2) a system for imitating object interactions in a physics simulator with reinforcement learning. We apply our reconstruction technique to 100 challenging Internet videos. We further show that we can successfully imitate a range of different object interactions in a physics simulator. Our object-centric approach is not limited to human-like end-effectors and can learn to imitate object interactions using different embodiments, like a robotic arm with a parallel jaw gripper.

This paper introduces the Generalized Action Governor, which is a supervisory scheme for augmenting a nominal closed-loop system with the capability of strictly handling constraints. After presenting its theory for general systems and introducing tailored design approaches for linear and discrete systems, we discuss its application to safe online learning, which aims to safely evolve control parameters using real-time data to improve performance for uncertain systems. In particular, we propose two safe learning algorithms based on integration of reinforcement learning/data-driven Koopman operator-based control with the generalized action governor. The developments are illustrated with a numerical example.

A high-quality 3D reconstruction of a scene from a collection of 2D images can be achieved through offline/online mapping methods. In this paper, we explore active mapping from the perspective of implicit representations, which have recently produced compelling results in a variety of applications. One of the most popular implicit representations - Neural Radiance Field (NeRF), first demonstrated photorealistic rendering results using multi-layer perceptrons, with promising offline 3D reconstruction as a by-product of the radiance field. More recently, researchers also applied this implicit representation for online reconstruction and localization (i.e. implicit SLAM systems). However, the study on using implicit representation for active vision tasks is still very limited. In this paper, we are particularly interested in applying the neural radiance field for active mapping and planning problems, which are closely coupled tasks in an active system. We, for the first time, present an RGB-only active vision framework using radiance field representation for active 3D reconstruction and planning in an online manner. Specifically, we formulate this joint task as an iterative dual-stage optimization problem, where we alternatively optimize for the radiance field representation and path planning. Experimental results suggest that the proposed method achieves competitive results compared to other offline methods and outperforms active reconstruction methods using NeRFs.

Mining genuine mechanisms underlying the complex data generation process in real-world systems is a fundamental step in promoting interpretability of, and thus trust in, data-driven models. Therefore, we propose a variation-based cause effect identification (VCEI) framework for causal discovery in bivariate systems from a single observational setting. Our framework relies on the principle of independence of cause and mechanism (ICM) under the assumption of an existing acyclic causal link, and offers a practical realization of this principle. Principally, we artificially construct two settings in which the marginal distributions of one covariate, claimed to be the cause, are guaranteed to have non-negligible variations. This is achieved by re-weighting samples of the marginal so that the resultant distribution is notably distinct from this marginal according to some discrepancy measure. In the causal direction, such variations are expected to have no impact on the effect generation mechanism. Therefore, quantifying the impact of these variations on the conditionals reveals the genuine causal direction. Moreover, we formulate our approach in the kernel-based maximum mean discrepancy, lifting all constraints on the data types of cause-and-effect covariates, and rendering such artificial interventions a convex optimization problem. We provide a series of experiments on real and synthetic data showing that VCEI is, in principle, competitive to other cause effect identification frameworks.

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches.

Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter $\rho$. Due to the absence of a general rule for setting $\rho$, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust $\rho$ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses $\rho$ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust $\rho$ considering the stage of the optimization process to accelerate the convergence speed further.

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field.