Full-Body Torque-Level Non-linear Model Predictive Control for Aerial Manipulation

Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.Comment: Submitted to Transactions on Robotics. 17 pages, 16 figure

Hierarchical task control through lexicographic semidefinite programming

Peer reviewe

Squash-box feasibility driven differential dynamic programming

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e. a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.This work was partially supported by the EU H2020 project GAUSS(H2020-Galileo-2017-1-776293), project EB-SLAM (DPI2017-89564-P),by the Spanish State Research Agency through the Mar ́ıa de Maeztu Sealof Excellence to IRI (MDM-2016-0656) and by the European Commissionunder the Horizon 2020 project Memory of Motion (MEMMO, projectID: 780684). Part of this research was carried out at the Jet PropulsionLaboratory, California Institute of Technology, under a contract with theNational Aeronautics and Space Administration (NASA, USPeer ReviewedPostprint (author's final draft

Multi-task closed-loop inverse kinematics stability through semidefinite programming

Trabajo presentado en la IEEE International Conference on Robotics and Automation (ICRA), celebrada de forma virtual en París (Francia) del 31 de mayo al 31 de agosto de 2020Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the local stability problem of a hierarchical closed-loop inverse kinematics algorithm for such highly redundant robots. We present a method to guarantee this system stability by performing an online tuning of the closed-loop control gains. We define a semi-definite programming problem (SDP) with these gains as decision variables and a discrete-time Lyapunov stability condition as a linear matrix inequality, constraining the SDP optimization problem and guaranteeing the local stability of the prioritized tasks. To the best of authors' knowledge, this work represents the first mathematical development of an SDP formulation that introduces these stability conditions for a multi-objective closed-loop inverse kinematic problem for highly redundant robots. The validity of the proposed approach is demonstrated through simulation case studies, including didactic examples and a Matlab toolbox for the benefit of the community

Multi-task closed-loop inverse kinematics stability through semidefinite programming

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Today’s complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a hierarchical closed-loop inverse kinematics algorithm for such highly redundant robots. We present a method to guarantee system stability by performing an online tuning of the closedloop control gains. We define a semi-definite programming problem (SDP) with these gains as decision variables and a discrete-time Lyapunov stability condition as a linear matrix inequality, constraining the SDP optimization problem and guaranteeing the stability of the prioritized tasks. To the best of authors’ knowledge, this work represents the first mathematical development of an SDP formulation that introduces stability conditions for a multi-objective closed-loop inverse kinematic problem for highly redundant robots. The validity of the proposed approach is demonstrated through simulation case studies, including didactic examples and a Matlab toolbox for the benefit of the community.This work was partially supported by the EU H2020 project GAUSS (H2020-Galileo-2017-1-776293), project EB-SLAM (DPI2017-89564-P) and by the Spanish State Research Agency through the Mar ́ıa de Maeztu Seal of Excellence to IRI (MDM-2016-0656). Part of this research was car-ried out at the Jet Propulsion Laboratory, California Institute of Technology,under a contract with the National Aeronautics and Space Administration(NASA, USA)Peer ReviewedPostprint (author's final draft