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Constrained Articulated Body Dynamics Algorithms

IEEE TRANSACTIONS ON ROBOTICS 2025年 41卷 430-449页

作者： Sathya, Ajay Suresha Carpentier, Justin PSL Res Univ Ecole Normale Super Inria Dept Informat F-75006 Paris France Katholieke Univ Leuven Dept Mech Engn MECO Res Team B-3001 Leuven Belgium Katholieke Univ Leuven Flanders Make B-3001 Leuven Belgium

Rigid-body dynamics algorithms have played an essential role in robotics development. By finely exploiting the underlying robot structure, they allow the computation of the robot kinematics, dynamics, and related physical quantities with low complexity, enabling their integration into chipsets with limited resources or their evaluation at very high frequency for demanding applications (e.g., model predictive control, large-scale simulation, reinforcement learning, etc.). While most of these algorithms operate on constraint-free settings, only a few have been proposed so far to adequately account for constrained dynamical systems while depicting low algorithmic complexity. In this article, we introduce a series of new algorithms with reduced (and lowest) complexity for the forward simulation of constrained dynamical systems. Notably, we revisit the so-called articulated body algorithm (ABA) and the Popov-Vereshchagin algorithm (PV) in the light of proximal-point optimization and introduce two new algorithms, called constrained ABA and proxPV. These two new algorithms depict linear complexities while being robust to singular cases (e.g., redundant constraints, singular constraints, etc.). We establish the connection with existing literature formulations, especially the relaxed formulation at the heart of the MuJoCo and Drake simulators. We also propose an efficient and new algorithm to compute the damped Delassus inverse matrix with the lowest known computational complexity. All these algorithms have been implemented inside the open-source framework Pinocchio and depict, on a wide range of robotic systems ranging from robot manipulators to complex humanoid robots, state-of-the-art performances compared to alternative solutions of the literature.

关键词： Heuristic algorithms Robots Robot kinematics Symmetric matrices Vectors Prediction algorithms Kinematics Computational efficiency Computational complexity Symbols Direct/inverse dynamics formulation dynamics humanoid robots optimization and optimal control

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A Tutorial on Distributed optimization for Cooperative Robotics: From Setups and Algorithms to Toolboxes and Research Directions

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PROCEEDINGS OF THE IEEE 2025年第1期113卷 40-65页

作者： Testa, Andrea Carnevale, Guido Notarstefano, Giuseppe Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

Several interesting problems in multirobot systems can be cast in the framework of distributed optimization. Examples include multirobot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this article, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.

关键词： optimization Robots Multi-robot systems Robot kinematics Surveillance Resource management Distributed algorithms Tutorials Formation control Vehicle routing Cooperating robots distributed optimization distributed robot systems optimization and optimal control

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Pushing Everything Everywhere All at Once: Probabilistic Prehensile Pushing

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IEEE ROBOTICS AND AUTOMATION LETTERS 2025年第5期10卷 4540-4547页

作者： Perugini, Patrizio Lundell, Jens Friedl, Katharina Kragic, Danica KTH SE-10044 Stockholm Sweden Flanders Make B-3001 Leuven Belgium Kungliga Tekn Hogskolan KTH Div Robot Percept & Learning SE-10044 Stockholm Brazil

We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory optimization formulation. The critical insight is recasting the external pushers (environment) as a discrete probability distribution instead of binary variables and minimizing the entropy of the distribution. The probabilistic reformulation allows all pushers to be used simultaneously, but at the optimum, the probability mass concentrates onto one due to the entropy minimization. We numerically compare our method against a state-of-the-art sampling-based baseline on a prehensile pushing task. The results demonstrate that our method finds trajectories 8 times faster and at a 20 times lower cost than the baseline. Finally, we demonstrate that a simulated and real Frank Panda robot can successfully manipulate different objects following the trajectories proposed by our method.

关键词： Friction Trajectory optimization Entropy Dynamics Gravity Vectors Torque Probabilistic logic Planning Manipulator dynamics Dexterous manipulation optimization and optimal control manipulation planning

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Globally optimal Inverse Kinematics as a Non-Convex Quadratically Constrained Quadratic Program

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第6期9卷 5998-6003页

作者： Votroubek, Tomas Kroupa, Tomas Czech Tech Univ Fac Elect Engn Dept Comp Sci Prague 2 Czech Republic

We show how to compute globally optimal solutions to inverse kinematics by formulating the problem as a non-convex quadratically constrained quadratic program. Our approach makes solving inverse kinematics instances of generic redundant manipulators feasible. We demonstrate the performance on randomly generated designs and real-world robots with up to ten revolute joints. The same technique can be used for manipulator design by introducing kinematic parameters as variables.

关键词： Kinematics optimization and optimal control redundant robots

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Fast Direct optimal control for Humanoids Based on Dynamics Representation in FPC Latent Space

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第4期9卷 3823-3830页

作者： Shimizu, Soya Ayusawa, Ko Venture, Gentiane Tokyo Univ Agr & Technol Grad Sch Engn Dept Mech Syst Engn Koganei Tokyo 1848588 Japan Natl Inst Adv Ind Sci & Technol Human Augmentat Res Ctr Kashiwa Chiba 2770082 Japan CNRS AIST JRL Joint Robot Lab UMI3218 RL Tsukuba Ibaraki 3058560 Japan Univ Tokyo Dept Mech Engn Bunkyo ku Tokyo 1138656 Japan

This study introduces a novel approach to Humanoid Robot Motion Generation using Functional Principal Component Analysis (FPCA) within the framework of Direct optimal control (DOC). FPCA efficiently compresses high-dimensional motion data, including ground reaction forces, into a low-dimensional space known as the FPC space. These low-dimensional elements preserve the essential characteristics of the original motions and allow for the synthesis of specific elements to create entirely new representations. By using these low-dimensional elements as optimization variables, we anticipated a significant reduction in computational time for motion generation. Experiments on the humanoid robot HRP-4 J, considering various objective functions, demonstrated the method's applicability for generating whole-body motions. The Root Mean Square Error (RMSE) for angle data between the proposed method and conventional methods yielded an average RMSE of 0.007 rd, indicating precise motion generation without compromising data characteristics. Moreover, the proposed method's computation time was 35.8 times faster than the conventional approach.

关键词： Human and humanoid motion analysis and synthesis whole-body motion planning and control optimization and optimal control

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Robust Jumping With an Articulated Soft Quadruped Via Trajectory optimization and Iterative Learning

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第1期9卷 255-262页

作者： Ding, Jiatao Sels, Mees A. van Loben Angelini, Franco Kober, Jens Della Santina, Cosimo Delft Univ Technol Dept Cognit Robot NL-2628 CD Delft Netherlands Univ Pisa Ctr Ric Enrico Piaggio I-56126 Pisa Italy Univ Pisa Dipartimento Ingn Informaz I-56126 Pisa Italy German Aerosp Ctr DLR Inst Robot & Mechatron D-82234 Wessling Germany

Quadrupeds deployed in real-world scenarios need to be robust to unmodelled dynamic effects. In this work, we aim to increase the robustness of quadrupedal periodic forward jumping (i.e., pronking) by unifying cutting-edge model-based trajectory optimization and iterative learning control. Using a reduced-order soft anchor model, the optimization-based motion planner generates the periodic reference trajectory. The controller then iteratively learns the feedforward control signal in a repetition process, without requiring an accurate full-body model. When enhanced by a continuous learning mechanism, the proposed controller can learn the control inputs without resetting the system at the end of each iteration. Simulations and experiments on a quadruped with parallel springs demonstrate that continuous jumping can be learned in a matter of minutes, with high robustness against various types of terrain.

关键词： Legged robots optimization and optimal control motion control

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Locomotion control With Slip Detection for Quadruped Robot, PongBot

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INTERNATIONAL JOURNAL OF control AUTOMATION AND SYSTEMS 2024年第12期22卷 3744-3752页

作者： Kim, Kyung-Hwan Kim, Jung-Yup Seoul Natl Univ Sci & Technol Dept Mech Design & Robot Engn 232 Gongneung Ro Seoul 01811 South Korea

Quadruped robots have excellent mobility, allowing them to overcome various terrains. For this reason, a growing body of research has explored quadruped robot locomotion control. Many prior studies have addressed state estimation for locomotion control. Most floating-body state estimations have used leg odometry, which assumes zero absolute velocity of the stance feet. However, this method may lead to inappropriate estimation when the stance feet slip. In this paper, we propose a novel slip detection method to increase the performance of body state estimation. In addition, we establish an entire locomotion control framework to validate the proposed method. Finally, we experimentally verify the proposed method by walking a quadruped robot, 'PongBot', weighing about 40 kgf, on uneven and soft terrain.

关键词： Legged robots optimization and optimal control sensor fusion

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A Novel Closed-Form Approach for Enhancing Efficiency in Pose Estimation From 3D Correspondences

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第2期9卷 1843-1850页

作者： Malis, Ezio Univ Cote dAzur ACENTAURI team Inria F-06902 Paris France

Determining the pose using 3D data captured from two distinct frames holds significant significance in various robotic applications such as odometry, simultaneous localization and mapping and place recognition. Typically, this pose is calculated through the resolution of a least-squares problem, which involves establishing correspondences between points, points and planes, or points and lines. This non-linear least-squares problem can be addressed either through iterative optimization or, with greater efficiency, through closed-form solutions achieved via polynomial system solvers. In this letter, the focus is on enhancing the computational efficiency of polynomial solvers utilizing resultants. The newly proposed methodology outperforms previous techniques in terms of speed, all while maintaining identical levels of accuracy and robustness. Through simulations and real-world experiments, we validate the superior precision and robustness of the proposed algorithm when compared with prior methods.

关键词： Localization optimization and optimal control SLAM Autonomous Vehicle Navigation

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Toward Globally optimal State Estimation Using Automatically Tightened Semidefinite Relaxations

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IEEE TRANSACTIONS ON ROBOTICS 2024年 40卷 4338-4358页

作者： Dumbgen, Frederike Holmes, Connor Agro, Ben Barfoot, Timothy PSL Univ Ecole Normale Super Inria F-75006 Paris France Univ Toronto Robot Inst Toronto ON M5S 1A1 Canada

In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted redundant constraints are required to obtain tight relaxations, and thus global optimality. These constraints are formulation-dependent and typically identified through a lengthy manual process. Instead, the present article suggests an automatic method to find a set of sufficient redundant constraints to obtain tightness, if they exist. We first propose an efficient feasibility check to determine if a given set of variables can lead to a tight formulation. Second, we show how to scale the method to problems of bigger size. At no point of the process do we have to find redundant constraints manually. We showcase the effectiveness of the approach, in simulation and on real datasets, for range-based localization and stereo-based pose estimation. We also reproduce semidefinite relaxations presented in recent literature and show that our automatic method always finds a smaller set of constraints sufficient for tightness than previously considered.

关键词： Global optimality localization optimization and optimal control optimization and optimal control robot safety robot safety optimization and optimal control robot safety

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Transformer-Based Model Predictive control: Trajectory optimization via Sequence Modeling

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第11期9卷 9820-9827页

作者： Celestini, Davide Gammelli, Daniele Guffanti, Tommaso D'Amico, Simone Capello, Elisa Pavone, Marco Politecn Torino Dept Mech & Aerosp Engn I-10129 Turin Italy Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA

Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the recursive solution of highly non-convex trajectory optimization problems, leading to high computational complexity and strong dependency on initialization. In this work, we present a unified framework to combine the main strengths of optimization-based and learning-based methods for MPC. Our approach entails embedding high-capacity, transformer-based neural network models within the optimization process for trajectory generation, whereby the transformer provides a near-optimal initial guess, or target plan, to a non-convex optimization problem. Our experiments, performed in simulation and the real world onboard a free flyer platform, demonstrate the capabilities of our framework to improve MPC convergence and runtime. Compared to purely optimization-based approaches, results show that our approach can improve trajectory generation performance by up to 75%, reduce the number of solver iterations by up to 45%, and improve overall MPC runtime by 7x without loss in performance.

关键词： optimization Transformers Costs Planning Trajectory optimization Runtime Predictive control optimization and optimal control deep learning methods machine learning for robot control

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