Quasi-Periodic Gaussian Process Predictive Iterative Learning Control
IITB-Monash Research Academy, IIT Bombay（IITB-蒙纳士研究学院，IIT博伊斯瓦尔）；Department of Mathematics, IIT Bombay（数学系，IIT博伊斯瓦尔）；Department of Electrical and Computer Systems Engineering, Monash University（电气与计算机系统工程系，蒙纳士大学）
Unnati Nigam, Radhendushka Srivastava, Faezeh Marzbanrad, Michael Burke
Repetitive motion tasks are common in robotics, but performance can degrade over time due to environmental changes and robot wear and tear. Iterative learning control (ILC) improves performance by using information from previous iterations to compensate for expected errors in future iterations. This work incorporates the use of Quasi-Periodic Gaussian Processes (QPGPs) into a predictive ILC framework to model and forecast disturbances and drift across iterations. Using a recent structural equation formulation of QPGPs, the proposed approach enables efficient inference with complexity $\mathcal{O}(p^3)$ instead of $\mathcal{O}(i^2p^3)$, where $p$ denotes the number of points within an iteration and $i$ represents the total number of iterations, specially for larger $i$. This formulation also enables parameter estimation without loss of information, making continual GP learning computationally feasible within the control loop. By predicting next-iteration error profiles rather than relying only on past errors, the controller achieves faster convergence and maintains this under time-varying disturbances. We benchmark the method against both standard ILC and conventional Gaussian Process (GP)-based predictive ILC on three tasks, autonomous vehicle trajectory tracking, a three-link robotic manipulator, and a real-world Stretch robot experiment. Across all cases, the proposed approach converges faster and remains robust under injected and natural disturbances while reducing computational cost. This highlights its practicality across a range of repetitive dynamical systems.
Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data
Institute of Financial Services Zug, Lucerne University of Applied Sciences and Arts（卢塞恩应用科学与艺术大学金融服务研究所）；Department of Mathematical Modeling and Machine Learning, University of Zurich（苏黎世大学数学建模与机器学习系）
Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the generalization error of a deep neural network and at the same time the minimization of its prediction time. We may also consider as a constraint that the deep neural network must be implemented in a chip with an area below some size. Here, both the objectives and the constraint are black boxes, i.e., functions whose analytical expressions are unknown and are …
School of Information Technologies, The University of Sydney（悉尼大学信息技术学院）；The University of Sydney（悉尼大学）
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large datasets often make modelling periodicity untenable for otherwise powerful non-parametric methods like Gaussian Processes (GPs) which typically incur an $\mathcal{O}(N^3)$ computational burden and, consequently, are unable to scale to larger datasets. To this end we introduce a method termed \emph{Index Set Fourier Series Features} to tractably exploit multiv…
Vector Institute for Artificial Intelligence（人工智能向量研究所）
In this work we address the problem of performing a repetitive task when we have uncertain observations and dynamics. We formulate this problem as an iterative infinite horizon optimal control problem with output feedback. Previously, this problem was solved for linear time-invariant (LTI) system for the case when noisy full-state measurements are available using a robust iterative learning control framework, which we refer to as robust learning-based model predictive control (RL-MPC). However, this work does not apply to the case when only noisy observations of part of the state are available…
We propose in this paper Periodic Interaction Primitives - a probabilistic framework that can be used to learn compact models of periodic behavior. Our approach extends existing formulations of Interaction Primitives to periodic movement regimes, i.e., walking. We show that this model is particularly well-suited for learning data-driven, customized models of human walking, which can then be used for generating predictions over future states or for inferring latent, biomechanical variables. We also demonstrate how the same framework can be used to learn controllers for a robotic prosthesis usin…
Pivoting gait is efficient for manipulating a big and heavy object with relatively small manipulating force, in which a robot iteratively tilts the object, rotates it around the vertex, and then puts it down to the floor. However, pivoting gait can easily fail even with a small external disturbance due to its instability in nature. To cope with this problem, we propose a controller to robustly control the object motion during the pivoting gait by introducing two gait modes, i.e., one is the double-support mode, which can manipulate a relatively light object with faster speed, and the other is …
Agile & Dexterous Robotics Lab, ETH Zürich（敏捷灵巧机器人实验室，苏黎世联邦理工学院）；Robotic Systems Lab, ETH Zürich（机器人系统实验室，苏黎世联邦理工学院）；ETH Zürich（苏黎世联邦理工学院（注：此处ETH Zürich是机构名，与前面实验室同属苏黎世联邦理工学院））
In this work we present a whole-body Nonlinear Model Predictive Control approach for Rigid Body Systems subject to contacts. We use a full dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences and timings are not prespecified but optimized by the solver. Yet, thorough numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state of the art by at least one order of magnitude. Hardware experiments in form of period…
Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots
Center for Robotics and Biosystems, Northwestern University（西北大学机器人与生物系统中心）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Department of Mechanical Engineering, Carnegie Mellon University（卡内基梅隆大学机械工程系）
Optimal control is often used in robotics for planning a trajectory to achieve some desired behavior, as expressed by the cost function. Most works in optimal control focus on finding a single optimal trajectory, which is then typically tracked by another controller. In this work, we instead consider trajectory distribution as the solution of an optimal control problem, resulting in better tracking performance and a more stable controller. A Gaussian distribution is first obtained from an iterative Linear Quadratic Regulator (iLQR) solver. A short horizon Model Predictive Control (MPC) is then…
Performing highly agile dynamic motions, such as jumping or running on uneven stepping stones has remained a challenging problem in legged robot locomotion. This paper presents a framework that combines trajectory optimization and model predictive control to perform robust and consecutive jumping on stepping stones. In our approach, we first utilize trajectory optimization based on full-nonlinear dynamics of the robot to generate periodic jumping trajectories for various jumping distances. A jumping controller based on a model predictive control is then designed for realizing smooth jumping tr…
