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Tuning and sensitivity analysis of a hexapod state estimator
Abstract
An important envisaged application of legged robots is the exploration and mapping of extreme environments with an unknown terrain. Corin is a hexapod designed at the University of Manchester, which is able to perform motions using footholds on surfaces perpendicular to the ground plane. This allows it to be able to navigate through confined and narrow spaces. The hexapod requires an accurate estimate of its pose in order to be able to perform these motions. Current state-of-the-art state estimators for legged robots that solely use proprioceptive sensors, fuse inertial and leg kinematic measurements through an extended Kalman filter (EKF). This paper describes the implementation and validation of a state estimator on the Corin hexapod whilst performing motions using surface perpendicular to the ground plane. Another novelty of the work is the analysis of the algorithm sensitivity to the filter parameters and motion variables, and the tuning of the EKF using particle swarm optimisation (PSO). The results show that the average error achieved was below 6% for both position and orientation estimates.
... Like for the DGSM, the advantage of this method, in comparison with the SSM and the LSM, is considering the influence of the motion of the robot in the capacity of keeping the torso upright instead of assuming quasi-static circumstances. Ref. [27] also used a Kalman filter to estimate the pose of the hexapod when walking across surfaces perpendicular to the ground. This algorithm estimated and corrected the body posture through the data provided by an IMU, the contact forces and the position of each joint and obtained better results than the respective dynamic model of the robot, even when foot slippage occurred. ...
... Most of the designed dynamic-based controllers mainly contained the definition of the interactions of the feet and used kinematic models for the rest of the control. One emergent solution for this problem was the implementation of predictive models to estimate the stability of the hexapod [9], its posture [27] or the safety of the ground through the value of the contact forces [29]. ...
The static stability of hexapods motivates their design for tasks in which stable locomotion is required, such as navigation across complex environments. This task is of high interest due to the possibility of replacing human beings in exploration, surveillance and rescue missions. For this application, the control system must adapt the actuation of the limbs according to their surroundings to ensure that the hexapod does not tumble during locomotion. The most traditional approach considers their limbs as robotic manipulators and relies on mechanical models to actuate them. However, the increasing interest in model-free models for the control of these systems has led to the design of novel solutions. Through a systematic literature review, this paper intends to overview the trends in this field of research and determine in which stage the design of autonomous and adaptable controllers for hexapods is.
... From the tripod gait to the pentagonal gait, although the robot slows down, the attitude fluctuation and yaw also basically decrease, which means the stability of the robot's motion is better. Since the quadrangular gait and the pentagonal gait require more steps, it may make the robot foot slip phenomenon more obvious to a certain extent, and increase the robot's walking distance error [36]. Combing the actual needs, users can set suitable gait types and parameters on the mobile device. ...
Gait is an important research content of hexapod robots. To better improve the motion performance of hexapod robots, many researchers have adopted some high-cost sensors or complex gait control algorithms. This paper studies the straight gait of a small electric hexapod robot with a low cost, which can be used in daily life. The strategy of “increasing duty factor” is put forward in the gait planning, which aims to reduce foot sliding and attitude fluctuation in robot motion. The straight gaits of the robot include tripod gait, quadrangular gait, and pentagonal gait, which can be described conveniently by discretization and a time sequence diagram. In order to facilitate the user to control the robot to achieve all kinds of motion, an online gait transformation algorithm based on the adjustment of foot positions is proposed. In addition, according to the feedback of the actual attitude information, a yaw angle correction algorithm based on kinematics analysis and PD controller is designed to reduce the motion error of the robot. The experiments show that the designed gait planning scheme and control algorithm are effective, and the robot can achieve the expected motion. The RMSE of the row, pitch, and yaw angle was reduced by 35%, 25%, and 12%, respectively, using the “increasing duty factor” strategy, and the yaw angle was limited in the range −3°~3° using the yaw angle correction algorithm. Finally, the comparison with related works and the limitations are discussed.
In this paper, we address motion efficiency in autonomous robot exploration with multi-legged walking robots that can traverse rough terrains at the cost of lower efficiency and greater body vibration. We propose a robotic system for online and incremental learning of the terrain traversal cost that is immediately utilized to reason about next navigational goals in building spatial model of the robot surrounding. The traversal cost experienced by the robot is characterized by incrementally constructed Gaussian Processes using Bayesian Committee Machine. During the exploration, the robot builds the spatial terrain model, marks untraversable areas, and leverages the Gaussian Process predictive variance to decide whether to improve the spatial model or decrease the uncertainty of the terrain traversal cost. The feasibility of the proposed approach has been experimentally verified in a fully autonomous deployment with the hexapod walking robot.
Advanced motions, which utilize footholds on walls, offer considerably more opportunities for hexapods in accessing confined environment. However, there has been no research on the practical application of such motions on a hexapod. These motions are kinematically viable for the standard hexapod design with three degrees of freedom per leg but the joint requirements have yet to be identified. This article presents the motion analysis for two forms of advanced motion, wall walking and chimney walking, to study the joint requirement for executing such motions. The analysis has been verified through a series of experiments demonstrating that a hexapod with a standard design is capable of executing advanced motions.
Traversing rough terrains is one of the domains where multi-legged walking robots benefit from their relatively more complex kinematics in comparison to wheeled robots. The complexity of walking robots is usually related not only to mechanical parts but also to servomotors and the necessary electronics to efficiently control such a robotic system. Therefore, large, middle, but even small walking robots capable of traversing rough terrains can be very costly because of all the required equipment. On the other hand, using intelligent servomotors with the position control and feedback, affordable hexapod walking robots are becoming increasingly available. However, additional sensors may still be needed to stabilize the robot motion on rough terrains, e.g., inclinometers or inertial measurement units, force or tactile sensors to detect the ground contact point of the leg foot-tip. In this work, we present a minimalistic approach for adaptive locomotion control using only the servomotors position feedback. Adaptive fine-tuning of the proposed controller is supported by a dynamic model of the robot leg accompanied by the model of the internal servomotor controller. The models enable timely detection of the leg contact point with the ground and reduce developed stress and torques applied to the robot construction and servomotors without any additional sensor feedback. The presented results support that the proposed approach reliably detects the ground contact point, and thus enable traversing rough terrains with small, affordable hexapod walking robot.
As legged robots are sent into unstructured environments, the ability to robustly manage contact transitions will be a critical skill. This paper introduces an approach to probabilistically fuse contact models, managing uncertainty in terrain geometry, dynamic modeling, and kinematics to improve the robustness of contact initiation at touchdown. A discrete-time extension of the generalized-momentum disturbance observer is presented to increase the accuracy of proprioceptive force control estimates. This information is fused with other contact priors under a framework of Kalman Filtering to increase robustness of the method. This approach results in accurate contact detection with 99.3 % accuracy and a small 4-5ms delay. Using this new detector, an Event-Based Finite State Machine is implemented to deal with unexpected early and late contacts. This allows the robot to traverse cluttered environments by modifying the control actions for each individual leg based on the estimated contact state rather than adhering to a rigid time schedule regardless of actual contact state. Experiments with the MIT Cheetah 3 robot show the success of both the detection algorithm, as well as the Event-Based FSM while making unexpected contacts during trotting.
In this paper we present a system for the state estimation of a dynamically walking and trotting quadruped. The approach fuses four heterogeneous sensor sources (inertial, kinematic, stereo vision and LIDAR) to maintain an accurate and consistent estimate of the robot's base link velocity and position in the presence of disturbances such as slips and missteps. We demonstrate the performance of our system, which is robust to changes in the structure and lighting of the environment, as well as the terrain over which the robot crosses. Our approach builds upon a modular inertial-driven Extended Kalman Filter which incorporates a rugged, probabilistic leg odometry component with additional inputs from stereo visual odometry and LIDAR registration. The simultaneous use of both stereo vision and LIDAR helps combat operational issues which occur in real applications. To the best of our knowledge, this paper is the first to discuss the complexity of consistent estimation of pose and velocity states, as well as the fusion of multiple exteroceptive signal sources at largely different frequencies and latencies, in a manner which is acceptable for a quadruped's feedback controller. A substantial experimental evaluation demonstrates the robustness and accuracy of our system, achieving continuously accurate localization and drift per distance traveled below 1 cm/m.
This paper concerns the self-localization problem of a hexapod walking robot operating in rough terrains. Given that legged robots exhibit higher terrain passability than wheeled or tracked platforms when operating in harsh environments, they constitute a challenge for the localization techniques because the camera motion between consecutive frames can be arbitrary due to the motion gait and terrain irregularities. In this paper, we present and evaluate an iner-tially assisted Stereo Parallel Tracking and Mapping (S-PTAM) method deployed on a hexapod crawling robot in a rough terrain. The considered deployment scenario is motivated by autonomous navigation in an unknown environment in an open loop fashion. The reported results and comparison with an existing RGB-D SLAM technique show the feasibility of the proposed approach and its suitability for navigation of crawlers in harsh environments.
As a main limitation in the state and parameters estimation using Extended Kalman Filter (EKF) is that its optimality is critically dependent on the choice of the right covariance matrices of state and measurement noise. In order to overcome this difficulty, a new approach based on the use of the tuned EKF to estimate simultaneously the speed and rotor flux of an induction motor drive is proposed. This approach will firstly optimize the covariance matrices by the Particle Swarm Optimization (PSO) algorithm and after that, the values of these covariance matrices are introduced in the estimation loop. Computer simulation results indicate an accurate estimation and an acceptable performance in speed-rotor flux estimation after considerable tuning of the covariance matrices coefficients and confirm the efficiency of our proposed method.
Nowadays, particle swarm optimisation (PSO) is one of the most commonly used optimisation techniques. However, PSO parameters significantly affect its computational behaviour. That is, while it exposes desirable computational behaviour with some settings, it does not behave so by some other settings, so the way for setting them is of high importance. This paper explains and discusses thoroughly about various existent strategies for setting PSO parameters, provides some hints for its parameter setting and presents some proposals for future research on this area. There exists no other paper in literature that discusses the setting process for all PSO parameters. Using the guidelines of this paper can be strongly useful for researchers in optimisation-related fields.
This paper presents a new approach of optimizing the performance of an Extended Kalman Filter (EKF) using particle swarm optimization (PSO) for speed estimation of an induction motor drive. The development of the EKF algorithm and selection of the filter covariance for the EKF based speed estimation are presented and discussed. The effectiveness of the optimization technique is verified through Matlab/Simulink simulation of a direct torque control (DTC) drive system under various operating conditions.
We report on a continuous time odometry scheme for a walking hexapod robot built upon a previously developed leg-strain based body pose estimator. We implement this estimation procedure and odometry scheme on the robot RHex and evaluate its performance at widely varying speeds and over different ground conditions by means of a 6 degree of freedom vision based ground truth measurement system (GTMS). We also compare the performance to that of sensorless odometry schemes — both legged as well as on a wheeled version of the robot — using GTMS measurements of elapsed distance.
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We report on a hybrid 12-dimensional full body state estimator for a hexapod robot executing a jogging gait in steady state on level terrain with regularly alternating ground contact and aerial phases of motion. We use a repeating sequence of continuous time dynamical models that are switched in and out of an extended Kalman filter to fuse measurements from a novel leg pose sensor and inertial sensors. Our inertial measurement unit supplements the traditionally paired three-axis rate gyro and three-axis accelerometer with a set of three additional three-axis accelerometer suites, thereby providing additional angular acceleration measurement, avoiding the need for localization of the accelerometer at the center of mass on the robot's body, and simplifying installation and calibration. We implement this estimation procedure offline, using data extracted from numerous repeated runs of the hexapod robot RHex (bearing the appropriate sensor suite) and evaluate its performance with reference to a visual ground-truth measurement system, comparing as well the relative performance of different fusion approaches implemented via different model sequences
In this manuscript, we tackle the problem of a continuous localization of a legged robot. We propose a novel, optimization-based procedure for the state estimation of the robot using measurements from internal sensors (legged odometry). Then, we propose the optimization-based integration of the legged odometry and the visual SLAM output. The proposed multi-modal localization system can continuously estimate the pose of the robot in various conditions despite fast motions of the robot, slippages or image motion blur. We provide the results of the real-time implementation of the proposed method on a multi-legged walking robot. We compare the proposed localization method to other state of the art localization systems and provide the dataset for future comparisons.
In the year 1995, Dr R.C. Eberhart, who was an electrical engineer, along with Dr. James Kennedy, a social psycologist invented a random optimization technique which a was later named as Particle Swarm Optimization. As the name itself asserts that this method draws inspiration from natural biotic life of swarms of flocks. It uses the same principle to find most optimal solution to problem in search space as birds do find their most suitable place in a flock or insects do in a swarm. The PSO algorithm is initialized with a horde of particles which are a collection of random feasible solutions. Every single particle in the swarm is initialised a random velocity and as soon as they are assigned a velocity these particles start moving in problem search space. Now from this space the algorithm draws the particle to most suited fitness which in turn pulls it to the location of best fitness achieved across the whole horde. The PSO update rule comprises of many distinguishing features which are adjusted and modified depending upon the area of application of algorithm. This paper gives a detailed description of the PSO algorithm and significance of the various parameters involved in its update rule. It also highlights the advantages and disadvantages of using PSO algorithm in any optimization problem.
Purpose
This paper aims to evaluate four different simultaneous localization and mapping (SLAM) systems in the context of localization of multi-legged walking robots equipped with compact RGB-D sensors. This paper identifies problems related to in-motion data acquisition in a legged robot and evaluates the particular building blocks and concepts applied in contemporary SLAM systems against these problems. The SLAM systems are evaluated on two independent experimental set-ups, applying a well-established methodology and performance metrics.
Design/methodology/approach
Four feature-based SLAM architectures are evaluated with respect to their suitability for localization of multi-legged walking robots. The evaluation methodology is based on the computation of the absolute trajectory error (ATE) and relative pose error (RPE), which are performance metrics well-established in the robotics community. Four sequences of RGB-D frames acquired in two independent experiments using two different six-legged walking robots are used in the evaluation process.
Findings
The experiments revealed that the predominant problem characteristics of the legged robots as platforms for SLAM are the abrupt and unpredictable sensor motions, as well as oscillations and vibrations, which corrupt the images captured in-motion. The tested adaptive gait allowed the evaluated SLAM systems to reconstruct proper trajectories. The bundle adjustment-based SLAM systems produced best results, thanks to the use of a map, which enables to establish a large number of constraints for the estimated trajectory.
Research limitations/implications
The evaluation was performed using indoor mockups of terrain. Experiments in more natural and challenging environments are envisioned as part of future research.
Practical implications
The lack of accurate self-localization methods is considered as one of the most important limitations of walking robots. Thus, the evaluation of the state-of-the-art SLAM methods on legged platforms may be useful for all researchers working on walking robots’ autonomy and their use in various applications, such as search, security, agriculture and mining.
Originality/value
The main contribution lies in the integration of the state-of-the-art SLAM methods on walking robots and their thorough experimental evaluation using a well-established methodology. Moreover, a SLAM system designed especially for RGB-D sensors and real-world applications is presented in details.
In recent years, MEMS inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost. Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information. These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales. To overcome this issue, inertial sensors are typically combined with additional sensors and models. In this tutorial we focus on the signal processing aspects of position and orientation estimation using inertial sensors. We discuss different modeling choices and a selected number of important algorithms. The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations. The quality of their estimates is illustrated using both experimental and simulated data.
Reliable state estimation is crucial for stable planning and control of legged locomotion. A fundamental component of a state estimator in legged platforms is Leg Odometry, which only requires information about kinematics and contacts. Many legged robots use dedicated sensors on each foot to detect ground contacts. However, this choice is impractical for many agile legged robots in field operations, as these sensors often degrade and break. Instead, this paper focuses on the development of a robust Leg Odometry module, which does not require contact sensors. The module estimates the probability of reliable contact and detects foot impacts using internal force sensing. This knowledge is then used to improve the kinematics-inertial state estimate of the robot’s base. We show how our approach can reach comparable performance to systems with foot sensors. Extensive experimental results lasting over one hour are presented on our 85 kg quadrupedal robot HyQ carrying out a variety of gaits.
This paper describes an algorithm for the probabilistic fusion of sensor data from a variety of modalities (inertial, kinematic and LIDAR) to produce a single consistent position estimate for a walking humanoid. Of specific interest is our approach for continuous LIDAR-based localization which maintains reliable drift-free alignment to a prior map using a Gaussian Particle Filter. This module can be bootstrapped by constructing the map on-the-fly and performs robustly in a variety of challenging field situations. We also discuss a two-tier estimation hierarchy which preserves registration to this map and other objects in the robot's vicinity while also contributing to direct low-level control of a Boston Dynamics Atlas robot. Extensive experimental demonstrations illustrate how the approach can enable the humanoid to walk over uneven terrain without stopping (for tens of minutes), which would otherwise not be possible. We characterize the performance of the estimator for each sensor modality and discuss the computational requirements.
This paper presents a thorough performance analysis of several variants of the feature-based visual navigation system that uses RGB-D data to estimate in real-time the trajectory of a freely moving sensor. The evaluation focuses on the advantages and problems that are associated with choosing a particular structure of the sensor-tracking front-end, employing particular feature detectors/descriptors, and optimizing the resulting trajectory treated as a graph of sensor poses. Moreover, a novel yet simple graph pruning algorithm is introduced, which enables to remove spurious edges from the pose-graph. The experimental evaluation is performed on two publicly available RGB-D data sets to ensure that our results are scientifically verifiable.
The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as ‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input–output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach – the extended EM algorithm – is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKF that uses the covariance estimates obtained from the proposed approaches.
The Kalman estimation technique is examined from the point of view of the asymptotic behavior of the errors in the estimates. It is shown that, under certain conditions, the mean-square errors may become unbounded with time, and that this divergence may or may not be correctable by increasing the intensity of process noise assumed in the filtering model General results are derived for multidimensional systems, and both "true" and "apparent" divergence are demonstrated by a simple scalar system. Divergence due to numerical inaccuracies is considered, and an example problem in orbital navigation is used to demonstrate divergence and its elimination.
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