State Estimation for Legged Robots - Consistent Fusion of Leg Kinematics and IMU

This paper introduces a state estimation framework for legged robots that allows estimating the full pose of the robot without making any assumptions about the geometrical structure of its environment. This is achieved by means of an Observability Constrained Extended Kalman Filter that fuses kinematic encoder data with on-board IMU measurements. By including the absolute position of all footholds into the filter state, simple model equations can be formulated which accurately capture the uncertainties associated with the intermittent ground contacts. The resulting filter simultaneously estimates the position of all footholds and the pose of the main body. In the algorithmic formulation, special attention is paid to the consistency of the linearized filter: it maintains the same observability properties as the nonlinear system, which is a prerequisite for accurate state estimation. The presented approach is implemented in simulation and validated experimentally on an actual quadrupedal robot

Robust Legged Robot State Estimation Using Factor Graph Optimization

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 drift during dynamic motions such as trotting. To this end, we present a factor graph optimization method for state estimation which tightly fuses and smooths inertial navigation, leg odometry and visual odometry. The effectiveness of the approach is demonstrated using the ANYmal quadruped robot navigating in a realistic outdoor industrial environment. This experiment included trotting, walking, crossing obstacles and ascending a staircase. The proposed approach decreased the relative position error by up to 55% and absolute position error by 76% compared to kinematic-inertial odometry.Comment: 8 pages, 12 figures. Accepted to RA-L + IROS 2019, July 201

A Factor Graph Approach to Multi-Camera Extrinsic Calibration on Legged Robots

Legged robots are becoming popular not only in research, but also in industry, where they can demonstrate their superiority over wheeled machines in a variety of applications. Either when acting as mobile manipulators or just as all-terrain ground vehicles, these machines need to precisely track the desired base and end-effector trajectories, perform Simultaneous Localization and Mapping (SLAM), and move in challenging environments, all while keeping balance. A crucial aspect for these tasks is that all onboard sensors must be properly calibrated and synchronized to provide consistent signals for all the software modules they feed. In this paper, we focus on the problem of calibrating the relative pose between a set of cameras and the base link of a quadruped robot. This pose is fundamental to successfully perform sensor fusion, state estimation, mapping, and any other task requiring visual feedback. To solve this problem, we propose an approach based on factor graphs that jointly optimizes the mutual position of the cameras and the robot base using kinematics and fiducial markers. We also quantitatively compare its performance with other state-of-the-art methods on the hydraulic quadruped robot HyQ. The proposed approach is simple, modular, and independent from external devices other than the fiducial marker.Comment: To appear on "The Third IEEE International Conference on Robotic Computing (IEEE IRC 2019)

State Estimation for a Humanoid Robot

This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in [1] on a quadruped platform by incorporating the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter (EKF) accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. The filter employs a sensor-based prediction model which uses inertial data from an IMU and corrects for integrated error using a kinematics-based measurement model which relies on joint encoders and a kinematic model to determine the relative position and orientation of the feet. A nonlinear observability analysis is performed on both the original and updated filters and it is concluded that the new filter significantly simplifies singular cases and improves the observability characteristics of the system. Results on simulated walking and squatting datasets demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.Comment: IROS 2014 Submission, IEEE/RSJ International Conference on Intelligent Robots and Systems (2014) 952-95

Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation

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 contact-inertial system follows a log-linear autonomous differential equation; hence, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory. Due to the log-linear form of the error dynamics, it is not necessary to perform a nonlinear observability analysis to show that when using an Inertial Measurement Unit (IMU) and contact sensors, the absolute position of the robot and a rotation about the gravity vector (yaw) are unobservable. We further augment the state of the developed InEKF with IMU biases, as the online estimation of these parameters has a crucial impact on system performance. We evaluate the convergence of the proposed system with the commonly used quaternion-based EKF observer using a Monte-Carlo simulation. In addition, our experimental evaluation using a Cassie-series bipedal robot shows that the contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in the system dynamics.Comment: Published in the proceedings of Robotics: Science and Systems 201

Cerberus: Low-Drift Visual-Inertial-Leg Odometry For Agile Locomotion

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 estimation drift to lower than 1% during long distance high speed locomotion. Our drift results are better than any other state estimation method using the same set of sensors reported in the literature. Moreover, our state estimator performs well even when the robot is experiencing large impacts and camera occlusion. The implementation of the state estimator, along with the datasets used to compute our results, are available at https://github.com/ShuoYangRobotics/Cerberus.Comment: 7 pages, 6 figures, submitted to IEEE ICRA 202

Visual-Inertial and Leg Odometry Fusion for Dynamic Locomotion

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 the inertial frame. However, these values have a considerable amount of latency due to image processing and optimization, while the rate of update is quite low which is not suitable for low-level control. To reduce the latency, we predict the VIO state estimate at the rate of the IMU measurements of the VIO sensor. The EKF module uses the base pose and linear velocity predicted by VIO, fuses them further with a second high-rate IMU and leg odometry measurements, and produces robot state estimates with a high frequency and small latency suitable for control. We integrate this lightweight estimation framework with a nonlinear model predictive controller and show successful implementation of a set of agile locomotion behaviors, including trotting and jumping at varying horizontal speeds, on a torque-controlled quadruped robot.Comment: Submitted to IEEE International Conference on Robotics and Automation (ICRA), 202

Unsupervised Contact Learning for Humanoid Estimation and Control

This work presents a method for contact state estimation using fuzzy clustering to learn contact probability for full, six-dimensional humanoid contacts. The data required for training is solely from proprioceptive sensors - endeffector contact wrench sensors and inertial measurement units (IMUs) - and the method is completely unsupervised. The resulting cluster means are used to efficiently compute the probability of contact in each of the six endeffector degrees of freedom (DoFs) independently. This clustering-based contact probability estimator is validated in a kinematics-based base state estimator in a simulation environment with realistic added sensor noise for locomotion over rough, low-friction terrain on which the robot is subject to foot slip and rotation. The proposed base state estimator which utilizes these six DoF contact probability estimates is shown to perform considerably better than that which determines kinematic contact constraints purely based on measured normal force.Comment: Submitted to the IEEE International Conference on Robotics and Automation (ICRA) 201

Unsupervised Contact Learning for Humanoid Estimation and Control

This work presents a method for contact state estimation using fuzzy clustering to learn contact probability for full, six-dimensional humanoid contacts. The data required for training is solely from proprioceptive sensors - endeffector contact wrench sensors and inertial measurement units (IMUs) - and the method is completely unsupervised. The resulting cluster means are used to efficiently compute the probability of contact in each of the six endeffector degrees of freedom (DoFs) independently. This clustering-based contact probability estimator is validated in a kinematics-based base state estimator in a simulation environment with realistic added sensor noise for locomotion over rough, low-friction terrain on which the robot is subject to foot slip and rotation. The proposed base state estimator which utilizes these six DoF contact probability estimates is shown to perform considerably better than that which determines kinematic contact constraints purely based on measured normal force.Comment: Submitted to the IEEE International Conference on Robotics and Automation (ICRA) 201