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The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot dynamics, and robustness to model uncertainties is achieved by relying on precise bounds on the model mismatch. In this paper, we propose a novel adaptive robust feedback linearization scheme able to compensate for model uncertainties without any a-priori knowledge on them, and we provide a theoretical proof of convergence under mild assumptions. We evaluate the method on a simulated RR robot. First, we consider a nominal model with known model mismatch, which allows us to compare our strategy with state-of-the-art uncertainty-aware methods. Second, we implement the proposed control law in combination with a learned model, for which uncertainty bounds are not available. Results show that our method leads to performance comparable to uncertainty-aware methods while requiring less prior knowledge.

Multi-agent systems are increasingly widespread in a range of application domains, with optimization and learning underpinning many of the tasks that arise in this context. Different approaches have been proposed to enable the cooperative solution of these optimization and learning problems, including first- and second-order methods, and dual (or Lagrangian) methods, all of which rely on consensus and message-passing. In this article we discuss these algorithms through the lens of non-expansive operator theory, providing a unifying perspective. We highlight the insights that this viewpoint delivers, and discuss how it can spark future original research.

Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model based on Gaussian Process (GP) Regression for the identification of the inverse dynamics of robotic manipulators. The proposed model relies on a novel multidimensional kernel, called \textit{Lagrangian Inspired Polynomial} (\kernelInitials{}) kernel. The \kernelInitials{} kernel is based on two main ideas. First, instead of directly modeling the inverse dynamics components, we model as GPs the kinetic and potential energy of the system. The GP prior on the inverse dynamics components is derived from those on the energies by applying the properties of GPs under linear operators. Second, as regards the energy prior definition, we prove a polynomial structure of the kinetic and potential energy, and we derive a polynomial kernel that encodes this property. As a consequence, the proposed model allows also to estimate the kinetic and potential energy without requiring any label on these quantities. Results on simulation and on two real robotic manipulators, namely a 7 DOF Franka Emika Panda, and a 6 DOF MELFA RV4FL, show that the proposed model outperforms state-of-the-art black-box estimators based both on Gaussian Processes and Neural Networks in terms of accuracy, generality and data efficiency. The experiments on the MELFA robot also demonstrate that our approach achieves performance comparable to fine-tuned model-based estimators, despite requiring less prior information.

In this paper we focus on the solution of online problems with time-varying, linear equality and inequality constraints. Our approach is to design a novel online algorithm by leveraging the tools of control theory. In particular, for the case of equality constraints only, using robust control we design an online algorithm with asymptotic convergence to the optimal trajectory, differently from the alternatives that achieve non-zero tracking error. When also inequality constraints are present, we show how to modify the proposed algorithm to account for the wind-up induced by the nonnegativity constraints on the dual variables. We report numerical results that corroborate the theoretical analysis, and show how the proposed approach outperforms state-of-the-art algorithms both with equality and inequality constraints.

In this paper, we propose to estimate the forward dynamics equations of mechanical systems by learning a model of the inverse dynamics and estimating individual dynamics components from it. We revisit the classical formulation of rigid body dynamics in order to extrapolate the physical dynamical components, such as inertial and gravitational components, from an inverse dynamics model. After estimating the dynamical components, the forward dynamics can be computed in closed form as a function of the learned inverse dynamics. We tested the proposed method with several machine learning models based on Gaussian Process Regression and compared them with the standard approach of learning the forward dynamics directly. Results on two simulated robotic manipulators, a PANDA Franka Emika and a UR10, show the effectiveness of the proposed method in learning the forward dynamics, both in terms of accuracy as well as in opening the possibility of using more structured~models.

In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (non-quadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and non-quadratic problems.

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance., Comment: 23 pages (main article: 14 pages; appendix: 9 pages), 18 figures; accepted for publication on Automatica; final accepted version

The energy sustainability of multi-access edge computing (MEC) platforms is here addressed by developing Energy-Aware job Scheduling at the Edge (EASE), a computing resource scheduler for edge servers co-powered by renewable energy resources and the power grid. The scenario under study involves the optimal allocation and migration of time-sensitive computing tasks in a resource-constrained internet of vehicles (IoV) context. This is achieved by tackling, as the main objective, the minimization of the carbon footprint of the edge network, whilst delivering adequate quality of service (QoS) to the end users (e.g., meeting task execution deadlines). EASE integrates i) a centralized optimization step, solved through model predictive control (MPC), to manage the renewable energy that is locally collected at the edge servers and their local computing resources, estimating their future availability, and ii) a distributed consensus step, solved via dual ascent in closed form, to reach agreement on service migrations. EASE is compared with four existing migration strategies. Quantitative results demonstrate its greater energy efficiency, which often gets close to complete carbon neutrality, while also improving the QoS., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

This paper proposes a framework to study the convergence of stochastic optimization and learning algorithms. The framework is modeled over the different challenges that these algorithms pose, such as (i) the presence of random additive errors (e.g. due to stochastic gradients), and (ii) random coordinate updates (e.g. due to asynchrony in distributed set-ups). The paper covers both convex and strongly convex problems, and it also analyzes online scenarios, involving changes in the data and costs. The paper relies on interpreting stochastic algorithms as the iterated application of stochastic operators, thus allowing us to use the powerful tools of operator theory. In particular, we consider operators characterized by additive errors with sub-Weibull distribution (which parameterize a broad class of errors by their tail probability), and random updates. In this framework we derive convergence results in mean and in high probability, by providing bounds to the distance of the current iteration from a solution of the optimization or learning problem. The contributions are discussed in light of federated learning applications., Comment: To appear in IEEE Transactions on Automatic Control

In this paper, we consider the use of black-box Gaussian process (GP) models for trajectory tracking control based on feedback linearization, in the context of mechanical systems. We considered two strategies. The first computes the control input directly by using the GP model, whereas the second computes the input after estimating the individual components of the dynamics. We tested the two strategies on a simulated manipulator with seven degrees of freedom, also varying the GP kernel choice. Results show that the second implementation is more robust w.r.t. the kernel choice and model inaccuracies. Moreover, as regards the choice of kernel, the obtained performance shows that the use of a structured kernel, such as a polynomial kernel, is advantageous, because of its effectiveness with both strategies.

In this paper, we propose a Model-Based Reinforcement Learning (MBRL) algorithm for Partially Measurable Systems (PMS), i.e., systems where the state can not be directly measured, but must be estimated through proper state observers. The proposed algorithm, named Monte Carlo Probabilistic Inference for Learning COntrol for Partially Measurable Systems (MC-PILCO4PMS), relies on Gaussian Processes (GPs) to model the system dynamics, and on a Monte Carlo approach to update the policy parameters. W.r.t. previous GP-based MBRL algorithms, MC-PILCO4PMS models explicitly the presence of state observers during policy optimization, allowing to deal PMS. The effectiveness of the proposed algorithm has been tested both in simulation and in two real systems., Comment: Accepted to 3rd Robot Learning Workshop: Grounding Machine Learning Development in the Real World (NeurIPS 2020)

We consider the problem of PMU-based state estimation combining information coming from ubiquitous power demand time series and only a limited number of PMUs. Conversely to recent literature in which synchrophasor devices are often assumed perfectly synchronized with the Coordinated Universal Time (UTC), we explicitly consider the presence of time-synchronization errors in the measurements due to different non-ideal causes such as imperfect satellite localization and internal clock inaccuracy. We propose a recursive Kalman-based algorithm which allows for the explicit offline computation of the expected performance and for the real-time compensation of possible frequency mismatches among different PMUs. Based on the IEEE C37.118.1 standard on PMUs, we test the proposed solution and compare it with alternative approaches on both synthetic data from the IEEE 123 node standard distribution feeder and real-field data from a small medium voltage distribution feeder located inside the EPFL campus in Lausanne., Comment: 10 page, 7 figures

In this paper, we propose, discuss, and validate an online Nonlinear Model Predictive Control (NMPC) method for multi-rotor aerial systems with arbitrarily positioned and oriented rotors which simultaneously addresses the local reference trajectory planning and tracking problems. This work brings into question some common modeling and control design choices that are typically adopted to guarantee robustness and reliability but which may severely limit the attainable performance. Unlike most of state of the art works, the proposed method takes advantages of a unified nonlinear model which aims to describe the whole robot dynamics by explicitly including a realistic physical description of the actuator dynamics and limitations. As a matter of fact, our solution does not resort to common simplifications such as: 1) linear model approximation, 2) cascaded control paradigm used to decouple the translational and the rotational dynamics of the rigid body, 3) use of low-level reactive trackers for the stabilization of the internal loop, and 4) unconstrained optimization resolution or use of fictitious constraints. More in detail, we consider as control inputs the derivatives of the propeller forces and propose a novel method to suitably identify the actuator limitations by leveraging experimental data. Differently from previous approaches, the constraints of the optimization problem are defined only by the real physics of the actuators, avoiding conservative -- and often not physical -- input/state saturations which are present, e.g., in cascaded approaches. The control algorithm is implemented using a state-of-the-art Real Time Iteration (RTI) scheme with partial sensitivity update method. CONTINUES..., Comment: cs.RO cs.SY math.OC math.DS

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based methods can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model.

In this paper, we introduce a novel data-driven inverse dynamics estimator based on Gaussian Process Regression. Driven by the fact that the inverse dynamics can be described as a polynomial function on a suitable input space, we propose the use of a novel kernel, called Geometrically Inspired Polynomial Kernel (GIP). The resulting estimator behaves similarly to model-based approaches as concerns data efficiency. Indeed, we proved that the GIP kernel defines a finite-dimensional Reproducing Kernel Hilbert Space that contains the inverse dynamics function computed through the Rigid Body Dynamics. The proposed kernel is based on the recently introduced Multiplicative Polynomial Kernel, a redefinition of the classical polynomial kernel equipped with a set of parameters that allows for a higher regularization. We tested the proposed approach in a simulated environment, and also in real experiments with a UR10 robot. The obtained results confirm that, compared to other data-driven estimators, the proposed approach is more data-efficient and exhibits better generalization properties. Instead, with respect to model-based estimators, our approach requires less prior information and is not affected by model bias.

We address the problem of distributed convex unconstrained optimization over networks characterized by asynchronous and possibly lossy communications. We analyze the case where the global cost function is the sum of locally coupled local strictly convex cost functions. As discussed in detail in a motivating example, this class of optimization objectives is, for example, typical in localization problems and in partition-based state estimation. Inspired by a generalized gradient descent strategy, namely the block Jacobi iteration, we propose a novel solution which is amenable for a distributed implementation and which, under a suitable condition on the step size, is provably locally resilient to communication failures. The theoretical analysis relies on the separation of time scales and Lyapunov theory. In addition, to show the flexibility of the proposed algorithm, we derive a resilient gradient descent iteration and a resilient generalized gradient for quadratic programming as two natural particularizations of our strategy. In this second case, global robustness is provided. Finally, the proposed algorithm is numerically tested on the IEEE 123 nodes distribution feeder in the context of partition-based smart grid robust state estimation in the presence of measurements outliers., Comment: 20 pages, 5 figures

A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that such a tightly-regulated profile, imposed for system design purposes and good operation of the network, should also guarantee a secure system, operating far from static bifurcation instabilities such as voltage collapse. In general however, these two objectives are distinct and must be separately enforced. We formulate an optimization problem which maximizes the distance to voltage collapse through injections of reactive power, subject to power flow and operational voltage constraints. By exploiting a linear approximation of the power flow equations we arrive at a convex reformulation which can be efficiently solved for the optimal injections. We also address the planning problem of allocating the resources by recasting our problem in a sparsity-promoting framework that allows us to choose a desired trade-off between optimality of injections and the number of required actuators. Finally, we present a distributed algorithm to solve the optimization problem, showing that it can be implemented on-line as a feedback controller. We illustrate the performance of our results with the IEEE30 bus network., Comment: 10 pages, 9 figures