Probabilistic Contact State Estimation for Legged Robots using Inertial Information
Institute of Computer Science, Foundation for Research and Technology - Hellas (FORTH)（希腊基础研究与技术基金会计算机科学研究所）；Ownage Dynamics L.P.（Ownage Dynamics有限合伙企业）
Michael Maravgakis, Despina-Ekaterini Argiropoulos, Stylianos Piperakis, Panos Trahanias
备注：
Accepted for publication at ICRA 2023, 7 pages, 10 figures
Legged robot navigation in unstructured and slippery terrains depends heavily on the ability to accurately identify the quality of contact between the robot's feet and the ground. Contact state estimation is regarded as a challenging problem and is typically addressed by exploiting force measurements, joint encoders and/or robot kinematics and dynamics. In contrast to most state of the art approaches, the current work introduces a novel probabilistic method for estimating the contact state based solely on proprioceptive sensing, as it is readily available by Inertial Measurement Units (IMUs) mounted on the robot's end effectors. Capitalizing on the uncertainty of IMU measurements, our method estimates the probability of stable contact. This is accomplished by approximating the multimodal probability density function over a batch of data points for each axis of the IMU with Kernel Density Estimation. The proposed method has been extensively assessed against both real and simulated scenarios on bipedal and quadrupedal robotic platforms such as ATLAS, TALOS and Unitree's GO1.
This paper introduces a novel proprioceptive state estimator for legged robots based on a learned displacement measurement from IMU data. Recent research in pedestrian tracking has shown that motion can be inferred from inertial data using convolutional neural networks. A learned inertial displacement measurement can improve state estimation in challenging scenarios where leg odometry is unreliable, such as slipping and compressible terrains. Our work learns to estimate a displacement measurement from IMU data which is then fused with traditional leg odometry. Our approach greatly reduces the …
This work reports on developing a deep inverse reinforcement learning method for legged robots terrain traversability modeling that incorporates both exteroceptive and proprioceptive sensory data. Existing works use robot-agnostic exteroceptive environmental features or handcrafted kinematic features; instead, we propose to also learn robot-specific inertial features from proprioceptive sensory data for reward approximation in a single deep neural network. Incorporating the inertial features can improve the model fidelity and provide a reward that depends on the robot's state during deployment…
X-IONet: Cross-Platform Inertial Odometry Network for Pedestrian and Legged Robot
Intelligent Transportation Thrust, The Hong Kong University of Science and Technology (Guangzhou)（科技大学（广州）智能交通研究组）；Intelligent Transportation Thrust and Artificial Intelligence Thrust, The Hong Kong University of Science and Technology (Guangzhou)（科技大学（广州）智能交通研究组和人工智能研究组）；Division of Emerging Interdisciplinary Areas, The Hong Kong University of Science and Technology（科技大学新兴交叉领域研究部）
College of Engineering, University of Michigan（密歇根大学工程学院）
The factor graph framework is a convenient modeling technique for robotic state estimation where states are represented as nodes, and measurements are modeled as factors. When designing a sensor fusion framework for legged robots, one often has access to visual, inertial, joint encoder, and contact sensors. While visual-inertial odometry has been studied extensively in this framework, the addition of a preintegrated contact factor for legged robots has been only recently proposed. This allowed for integration of encoder and contact measurements into existing factor graphs, however, new nodes h…
Oxford Robotics Institute（牛津机器人研究所）；University of Oxford（牛津大学）
Legged robots, specifically quadrupeds, are becoming increasingly attractive for industrial applications such as inspection. However, to leave the laboratory and to become useful to an end user requires reliability in harsh conditions. From the perspective of state estimation, it is essential to be able to accurately estimate the robot's state despite challenges such as uneven or slippery terrain, textureless and reflective scenes, as well as dynamic camera occlusions. We are motivated to reduce the dependency on foot contact classifications, which fail when slipping, and to reduce position dr…
Georgia Institute of Technology（佐治亚理工学院）；Florida Institute for Human & Machine Cognition（佛罗里达人机认知研究所）；University of West Florida（西佛罗里达大学）
Legged robot locomotion is a challenging task due to a myriad of sub-problems, such as the hybrid dynamics of foot contact and the effects of the desired gait on the terrain. Accurate and efficient state estimation of the floating base and the feet joints can help alleviate much of these issues by providing feedback information to robot controllers. Current state estimation methods are highly reliant on a conjunction of visual and inertial measurements to provide real-time estimates, thus being handicapped in perceptually poor environments. In this work, we show that by leveraging the kinemati…
College of Engineering, University of Michigan（密歇根大学工程学院）
This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on approximations of the system dynamics, such as an Extended Kalman Filter (EKF), which uses a system's Jacobian linearization along the current best estimate of its trajectory. On the basis of the theory of invariant observer design by Barrau and Bonnabel, and in particular, the Invariant EKF (InEKF), we show that the error dynamics of the point co…
University of Michigan（密歇根大学）；University of California, Berkeley（加州大学伯克利分校）
This paper proposes a state estimator for legged robots operating in slippery environments. An Invariant Extended Kalman Filter (InEKF) is implemented to fuse inertial and velocity measurements from a tracking camera and leg kinematic constraints. {\color{black}The misalignment between the camera and the robot-frame is also modeled thus enabling auto-calibration of camera pose.} The leg kinematics based velocity measurement is formulated as a right-invariant observation. Nonlinear observability analysis shows that other than the rotation around the gravity vector and the absolute position, all…
Planning safe motions for legged robots requires sophisticated safety verification tools. However, designing such tools for such complex systems is challenging due to the nonlinear and high-dimensional nature of these systems' dynamics. In this letter, we present a probabilistic verification framework for legged systems, which evaluates the safety of planned trajectories by learning an assessment function from trajectories collected from a closed-loop system. Our approach does not require an analytic expression of the closed-loop dynamics, thus enabling safety verification of systems with comp…
Among small-scale mobile robots, multi-modal locomotion can help compensate for limited actuator capabilities. However, supporting multiple locomotion modes or gaits in small terrestrial robots typically requires complex designs with low locomotion efficiency. In this work, legged and rolling gaits are achieved by a 10~cm robot having just two degrees of freedom (DoF). This is acheived by leg shaping that facilitates whole body rolling and event-driven control that maintains motion using simple inertial sensor measurements. Speeds of approximately 0.4 and 2.2 body lengths per second are achiev…
Multi-Domain Motion Embedding: Expressive Real-Time Mimicry for Legged Robots
Robotic Systems Lab, ETH Zurich, Zurich, Switzerland（苏黎世联邦理工学院机器人系统实验室）；Computational Robotics Lab, ETH Zurich, Zurich, Switzerland（苏黎世联邦理工学院计算机器人实验室）；ETH Zürich（苏黎世联邦理工学院）
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）；Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
Implementing dynamic locomotion behaviors on legged robots requires a high-quality state estimation module. Especially when the motion includes flight phases, state-of-the-art approaches fail to produce reliable estimation of the robot posture, in particular base height. In this paper, we propose a novel approach for combining visual-inertial odometry (VIO) with leg odometry in an extended Kalman filter (EKF) based state estimator. The VIO module uses a stereo camera and IMU to yield low-drift 3D position and yaw orientation and drift-free pitch and roll orientation of the robot base link in t…
Terrain-Awared LiDAR-Inertial Odometry for Legged-Wheel Robots Based on Radial Basis Function Approximation
School of Automation and Intelligent Sensing, Institute of Medical Robotics, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education（自动化与智能感知学院、医学机器人研究院、上海交通大学，系统控制与信息处理重点实验室）
We present an open-source Visual-Inertial-Leg Odometry (VILO) state estimation solution, Cerberus, for legged robots that estimates position precisely on various terrains in real time using a set of standard sensors, including stereo cameras, IMU, joint encoders, and contact sensors. In addition to estimating robot states, we also perform online kinematic parameter calibration and contact outlier rejection to substantially reduce position drift. Hardware experiments in various indoor and outdoor environments validate that calibrating kinematic parameters within the Cerberus can reduce estimati…
In this paper, we propose a visual-inertial framework able to efficiently estimate the camera poses of a non-rigid trinocular baseline for long-range depth estimation on-board a fast moving aerial platform. The estimation of the time-varying baseline is based on relative inertial measurements, a photometric relative pose optimizer, and a probabilistic wing model fused in an efficient Extended Kalman Filter (EKF) formulation. The estimated depth measurements can be integrated into a geo-referenced global map to render a reconstruction of the environment useful for local replanning algorithms. B…
A Survey of Legged Robotics in Non-Inertial Environments: Past, Present, and Future
School of Mechanical Engineering, Purdue University（帕克大学机械工程学院）；Department of Mechanical and Aerospace Engineering, Rutgers University（新泽西罗格斯大学机械与航空航天工程系）；Department of Robotics, University of Michigan（密歇根大学机器人系）
University of Oxford（牛津大学）；KTH Royal Institute of Technology（KTH皇家理工学院）；Scania AB（斯堪尼亚公司）
We present an efficient multi-sensor odometry system for mobile platforms that jointly optimizes visual, lidar, and inertial information within a single integrated factor graph. This runs in real-time at full framerate using fixed lag smoothing. To perform such tight integration, a new method to extract 3D line and planar primitives from lidar point clouds is presented. This approach overcomes the suboptimality of typical frame-to-frame tracking methods by treating the primitives as landmarks and tracking them over multiple scans. True integration of lidar features with standard visual feature…
California Institute of Technology（加州理工学院）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Northeastern University（东北大学）
There have been several successful implementations of bio-inspired legged robots that can trot, walk, and hop robustly even in the presence of significant unplanned disturbances. Despite all of these accomplishments, practical control and high-level decision-making algorithms in multi-modal legged systems are overlooked. In nature, animals such as birds impressively showcase multiple modes of mobility including legged and aerial locomotion. They are capable of performing robust locomotion over large walls, tight spaces, and can recover from unpredictable situations such as sudden gusts or slip…
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Huazhong University of Science and Technology（华中科技大学）；Hong Kong University of Science and Technology（香港科技大学）
Aerial surveillance and monitoring demand both real-time and robust motion detection from a moving camera. Most existing techniques for drones involve sending a video data streams back to a ground station with a high-end desktop computer or server. These methods share one major drawback: data transmission is subjected to considerable delay and possible corruption. Onboard computation can not only overcome the data corruption problem but also increase the range of motion. Unfortunately, due to limited weight-bearing capacity, equipping drones with computing hardware of high processing capabilit…
Probabilistic approach to feedback control enhances multi-legged locomotion on rugged landscapes
Institute for Robotics and Intelligent Machines（机器人与智能机器研究所）；Georgia Institute of Technology（佐治亚理工学院）；School of Physic（物理学院）；School of Mechanical Engineering（机械工程学院）
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；NVIDIA Research（英伟达研究）；Princeton University（普林斯顿大学）；Department of Mechanical Engineering, University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校机械工程系）
Legged robot locomotion on a dynamic rigid surface (i.e., a rigid surface moving in the inertial frame) involves complex full-order dynamics that is high-dimensional, nonlinear, and time-varying. Towards deriving an analytically tractable dynamic model, this study theoretically extends the reduced-order linear inverted pendulum (LIP) model from legged locomotion on a stationary surface to locomotion on a dynamic rigid surface (DRS). The resulting model is herein termed as DRS-LIP. Furthermore, this study introduces an approximate analytical solution of the proposed DRS-LIP that is computationa…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；Purdue University（普渡大学）；University of Rhode Island（罗德岛大学）
State estimation for legged locomotion over a dynamic rigid surface (DRS), which is a rigid surface moving in the world frame (e.g., ships, aircraft, and trains), remains an under-explored problem. This paper introduces an invariant extended Kalman filter that estimates the robot's pose and velocity during DRS locomotion by using common sensors of legged robots (e.g., inertial measurement units (IMU), joint encoders, and RDB-D camera). A key feature of the filter lies in that it explicitly addresses the nonstationary surface-foot contact point and the hybrid robot behaviors. Another key featur…
We present a sim-to-real framework that uses dynamics and domain randomized offline reinforcement learning to enhance open-loop gaits for legged robots, allowing them to traverse uneven terrain without sensing foot impacts. Our approach, D$^2$-Randomized Gait Modulation with Bezier Curves (D$^2$-GMBC), uses augmented random search with randomized dynamics and terrain to train, in simulation, a policy that modifies the parameters and output of an open-loop Bezier curve gait generator for quadrupedal robots. The policy, using only inertial measurements, enables the robot to traverse unknown roug…
Sensor Configuration Matters: A Systematic Evaluation of Multimodal SLAM on Quadruped Robots
Machine Intelligence and Robotics Lab, Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院智能机器人实验室）；Institute for Intelligent Systems, Esslingen University of Applied Sciences（埃森堡应用科学大学智能系统研究所）；Department of Computer Science, University of Freiburg（弗赖堡大学计算机科学系）
RMIT University（皇家墨尔本理工大学）；Australia National University（澳大利亚国立大学）；University of Melbourne（墨尔本大学）
Robust aiding of inertial navigation systems in GNSS-denied environments is critical for the removal of accumulated navigation error caused by the drift and bias inherent in inertial sensors. One way to perform such an aiding uses matching of geophysical measurements, such as gravimetry, gravity gradiometry or magnetometry, with a known geo-referenced map. Although simple in concept, this map matching procedure is challenging: the measurements themselves are noisy; their associated spatial location is uncertain; and the measurements may match multiple points within the map (i.e. non-unique sol…
University of Michigan（密歇根大学）；Toyota Research Institute（丰田研究院）
State-of-the-art robotic perception systems have achieved sufficiently good performance using Inertial Measurement Units (IMUs), cameras, and nonlinear optimization techniques, that they are now being deployed as technologies. However, many of these methods rely significantly on vision and often fail when visual tracking is lost due to lighting or scarcity of features. This paper presents a state-estimation technique for legged robots that takes into account the robot's kinematic model as well as its contact with the environment. We introduce forward kinematic factors and preintegrated contact…
Breaking speed scaling in quadrupedal robots via Huygens' coupled-pendulum dynamics
Center for X-Mechanics, Zhejiang University（浙江大学交叉力学中心）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学杭州国际科创中心）；Mirrorme Technology Co., Ltd.（魔镜科技有限公司）
ETH Zurich（苏黎世联邦理工学院）；University of Nevada, Reno（内华达大学雷诺分校）；Norwegian University of Science and Technology（挪威科技大学）；Flyability（Flyability公司）；Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
Autonomous exploration of subterranean environments constitutes a major frontier for robotic systems as underground settings present key challenges that can render robot autonomy hard to achieve. This has motivated the DARPA Subterranean Challenge, where teams of robots search for objects of interest in various underground environments. In response, the CERBERUS system-of-systems is presented as a unified strategy towards subterranean exploration using legged and flying robots. As primary robots, ANYmal quadruped systems are deployed considering their endurance and potential to traverse challe…
Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
In this paper, we present a factor-graph LiDAR-SLAM system which incorporates a state-of-the-art deeply learned feature-based loop closure detector to enable a legged robot to localize and map in industrial environments. These facilities can be badly lit and comprised of indistinct metallic structures, thus our system uses only LiDAR sensing and was developed to run on the quadruped robot's navigation PC. Point clouds are accumulated using an inertial-kinematic state estimator before being aligned using ICP registration. To close loops we use a loop proposal mechanism which matches individual …
This paper proposes a novel inertial-aided localization approach by fusing information from multiple inertial measurement units (IMUs) and exteroceptive sensors. IMU is a low-cost motion sensor which provides measurements on angular velocity and gravity compensated linear acceleration of a moving platform, and widely used in modern localization systems. To date, most existing inertial-aided localization methods exploit only one single IMU. While the single-IMU localization yields acceptable accuracy and robustness for different use cases, the overall performance can be further improved by usin…
