State Estimation for Quadruped Robots on Non-Stationary Terrain via Invariant Extended Kalman Filter and Disturbance Observer

Quadruped robots possess significant mobility in complex and uneven terrains due to their outstanding stability and flexibility, making them highly suitable in rescue missions, environmental monitoring, and smart agriculture. With the increasing use of quadruped robots in more demanding scenarios, ensuring accurate and stable state estimation in complex environments has become particularly important. Existing state estimation algorithms relying on multi-sensor fusion, such as those using IMU, LiDAR, and visual data, often face challenges on non-stationary terrains due to issues like foot-end slippage or unstable contact, leading to significant state drift. To tackle this problem, this paper introduces a state estimation algorithm that integrates an invariant extended Kalman filter (InEKF) with a disturbance observer, aiming to estimate the motion state of quadruped robots on non-stationary terrains. Firstly, foot-end slippage is modeled as a deviation in body velocity and explicitly included in the state equations, allowing for a more precise representation of how slippage affects the state. Secondly, the state update process integrates both foot-end velocity and position observations to improve the overall accuracy and comprehensiveness of the estimation. Lastly, a foot-end contact probability model, coupled with an adaptive covariance adjustment strategy, is employed to dynamically modulate the influence of the observations. These enhancements significantly improve the filter's robustness and the accuracy of state estimation in non-stationary terrain scenarios. Experiments conducted with the Jueying Mini quadruped robot on various non-stationary terrains show that the enhanced InEKF method offers notable advantages over traditional filters in compensating for foot-end slippage and adapting to different terrains.

A Multi-Sensor Fusion Underwater Localization Method Based on Unscented Kalman Filter on Manifolds

In recent years, the simplified computation of position and velocity changes in nonlinear systems using Lie groups and Lie algebra has been widely used in the study of robot localization systems. The unscented Kalman filter (UKF) can effectively deal with nonlinear systems through the unscented transformation, and in order to more accurately describe the robot localization system, the UKF method based on Lie groups has been studied successively. The computational complexity of the UKF on Lie groups is high, and in order to simplify its computation, the Lie groups are applied to the manifold, which efficiently handles the state and uncertainty and ensures that the system maintains the geometric constraints and computational simplicity during the updating process. In this paper, a multi-sensor fusion localization method based on an unscented Kalman filter on manifolds (UKF-M) is investigated. Firstly, a system model and a multi-sensor model are established based on an Autonomous Underwater Vehicle (AUV), and a corresponding UKF-M is designed for the system. Secondly, the multi-sensor fusion method is designed, and the fusion method is applied to the UKF-M. Finally, the proposed method is validated using an underwater cave dataset. The experiments demonstrate that the proposed method is suitable for underwater environments and can significantly correct the cumulative error in the trajectory estimation to achieve accurate underwater localization.

Control and evaluation of a humanoid robot with rolling contact joints on its lower body

In this paper, we introduce a new teen-sized humanoid platform dubbed DRACO 3, custom-built by Apptronik and altered for practical use by the Human Centered Robotics Laboratory at The University of Texas at Austin. The form factor of DRACO 3 is such that it can operate safely in human environments while reaching objects at human heights. To approximate the range of motion of humans, this robot features proximal actuation and mechanical artifacts to provide a high range of hip, knee, and ankle motions. In particular, rolling contact mechanisms on the lower body are incorporated using a proximal actuation principle to provide an extensive vertical pose workspace. To enable DRACO 3 to perform dexterous tasks while dealing with these complex transmissions, we introduce a novel whole-body controller (WBC) incorporating internal constraints to model the rolling motion behavior. In addition, details of our WBC for DRACO 3 are presented with an emphasis on practical points for hardware implementation. We perform a design analysis of DRACO 3, as well as empirical evaluations under the lens of the Centroidal Inertia Isotropy (CII) design metric. Lastly, we experimentally validate our design and controller by testing center of mass (CoM) balancing, one-leg balancing, and stepping-in-place behaviors.

Enhanced Autonomous Vehicle Positioning Using a Loosely Coupled INS/GNSS-Based Invariant-EKF Integration

High-precision navigation solutions are a main requirement for autonomous vehicle (AV) applications. Global navigation satellite systems (GNSSs) are the prime source of navigation information for such applications. However, some places such as tunnels, underpasses, inside parking garages, and urban high-rise buildings suffer from GNSS signal degradation or unavailability. Therefore, another system is required to provide a continuous navigation solution, such as the inertial navigation system (INS). The vehicle's onboard inertial measuring unit (IMU) is the main INS input measurement source. However, the INS solution drifts over time due to IMU-associated errors and the mechanization process itself. Therefore, INS/GNSS integration is the proper solution for both systems' drawbacks. Traditionally, a linearized Kalman filter (LKF) such as the extended Kalman filter (EKF) is utilized as a navigation filter. The EKF deals only with the linearized errors and suppresses the higher orders using the Taylor expansion up to the first order. This paper introduces a loosely coupled INS/GNSS integration scheme using the invariant extended Kalman filter (IEKF). The IEKF state estimate is independent of the Jacobians that are derived in the EKF; instead, it uses the matrix Lie group. The proposed INS/GNSS integration using IEKF is applied to a real road trajectory for performance validation. The results show a significant enhancement when using the proposed system compared to the traditional INS/GNSS integrated system that uses EKF in both GNSS signal presence and blockage cases. The overall trajectory 2D-position RMS error reduced from 19.4 m to 3.3 m with 82.98% improvement and the 2D-position max error reduced from 73.9 m to 14.2 m with 80.78% improvement.

Progress in symmetry preserving robot perception and control through geometry and learning

This article reports on recent progress in robot perception and control methods developed by taking the symmetry of the problem into account. Inspired by existing mathematical tools for studying the symmetry structures of geometric spaces, geometric sensor registration, state estimator, and control methods provide indispensable insights into the problem formulations and generalization of robotics algorithms to challenging unknown environments. When combined with computational methods for learning hard-to-measure quantities, symmetry-preserving methods unleash tremendous performance. The article supports this claim by showcasing experimental results of robot perception, state estimation, and control in real-world scenarios.

Design and simulation analysis of a bionic ostrich robot

To look for the reason why the biped animal in nature can run with such high speed and to design a bionic biped prototype which can behave the high speed running and jumping ability, this paper takes the fastest bipedal animal in nature: ostrich as the research subject. Firstly, the body structure and motion characteristics of ostrich are investigated. Secondly, a simple mechanical structure of bionic ostrich robot is designed based on the above biological investigated results. The robot is under-actuated with one actuator each leg, with a spring on the tarsometatarsus and a torsion spring on the metatarsophalangeal joint at the foot end. And then the mechanical design of leg structure is optimized. Finally, the high-speed running and jumping running gait is planned, and comparative simulations are implemented with different design requirements among pure rigid and rigid-flexible coupling scheme, which are rigid, only with spring, only with torsion spring, and with spring and torsion spring both, in detail. Simulation results show that the rigid-flexible coupling design scheme and whole body motion coordination can achieve better high speed performance. It provides an insight for the design and control of legged robots.

Map Construction and Path Planning Method for a Mobile Robot Based on Multi-Sensor Information Fusion

In order to solve the path planning problem of an intelligent vehicle in an unknown environment, this paper proposes a map construction and path planning method for mobile robots based on multi-sensor information fusion. Firstly, the extended Kalman filter (EKF) is used to fuse the ambient information of LiDAR and a depth camera. The pose and acceleration information of the robot is obtained through the pose sensor. The SLAM algorithm based on a fusion of LiDAR, a depth camera, and the inertial measurement unit was built. Secondly, the improved ant colony algorithm was used to carry out global path planning. Meanwhile, the dynamic window method was used to realize local planning and local obstacle avoidance. Finally, experiments were carried out on a robot platform to verify the reliability of the proposed method. The experiment results showed that the map constructed by multi-sensor information fusion was closer to the real environment, and the accuracy and robustness of SLAM were effectively improved. The turning angle of the path was smoothed using the improved ant colony algorithm, and the real-time obstacle avoidance was able to be realized using the dynamic window method. The efficiency of path planning was improved, and the automatic feedback control of the intelligent vehicle was able to be realized.

Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

Navigating by touch: haptic Monte Carlo localization via geometric sensing and terrain classification

Legged robot navigation in extreme environments can hinder the use of cameras and lidar due to darkness, air obfuscation or sensor damage, whereas proprioceptive sensing will continue to work reliably. In this paper, we propose a purely proprioceptive localization algorithm which fuses information from both geometry and terrain type to localize a legged robot within a prior map. First, a terrain classifier computes the probability that a foot has stepped on a particular terrain class from sensed foot forces. Then, a Monte Carlo-based estimator fuses this terrain probability with the geometric information of the foot contact points. Results demonstrate this approach operating online and onboard an ANYmal B300 quadruped robot traversing several terrain courses with different geometries and terrain types over more than 1.2 km. The method keeps pose estimation error below 20 cm using a prior map with trained network and using sensing only from the feet, leg joints and IMU.

Error-state Kalman filter for lower-limb kinematic estimation: Evaluation on a 3-body model

Human lower-limb kinematic measurements are critical for many applications including gait analysis, enhancing athletic performance, reducing or monitoring injury risk, augmenting warfighter performance, and monitoring elderly fall risk, among others. We present a new method to estimate lower-limb kinematics using an error-state Kalman filter that utilizes an array of body-worn inertial measurement units (IMUs) and four kinematic constraints. We evaluate the method on a simplified 3-body model of the lower limbs (pelvis and two legs) during walking using data from simulation and experiment. Evaluation on this 3-body model permits direct evaluation of the ErKF method without several confounding error sources from human subjects (e.g., soft tissue artefacts and determination of anatomical frames). RMS differences for the three estimated hip joint angles all remain below 0.2 degrees compared to simulation and 1.4 degrees compared to experimental optical motion capture (MOCAP). RMS differences for stride length and step width remain within 1% and 4%, respectively compared to simulation and 7% and 5%, respectively compared to experiment (MOCAP). The results are particularly important because they foretell future success in advancing this approach to more complex models for human movement. In particular, our future work aims to extend this approach to a 7-body model of the human lower limbs composed of the pelvis, thighs, shanks, and feet.