Accurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg convention and used the Stewart platform Tiger 66.1 developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per Least Square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform's center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The Target poses and Actual poses are then compared, and the error compensations are estimated using the Least-Squared methods to calculate the Predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements.

Researchers have studied Stewart-Gough platforms, also known as Gough-Stewart platforms or hexapod platforms extensively for their inherent fine control characteristics. Their studies led to the potential deployment opportunities of Stewart-Gough Platforms in many critical applications such as the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. Some of these applications need micro and nano-level movement control in 3D space for the motions to be precise, complicated, and repeatable; a Stewart-Gough platform fulfills these challenges smartly. For this, the platform must be more accurate than the specified application accuracy level and thus proper calibration for a parallel robot is crucial. Forward kinematics-based calibration for these hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To experiment with different calibration techniques, various calibration approaches were implemented by using external instruments, constraining one or more motions of the system, and using extra sensors for auto or self-calibration. This survey paid attention to those key methodologies, their outcome, and important details related to inverse kinematic-based parallel robot calibrations. It was observed during this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by one source or multiple sources. The error sources considered are mainly kinematic and structural, in some cases, environmental factors also are reviewed, however, those calibrations are done under no-load conditions. This study aims to review the present state of the art in this field and highlight the processes and errors considered for the calibration of Stewart-Gough platforms.

Stewart platform-based Parallel Kinematic (PKM) Machines have been extensively studied by researchers due to their inherent finer control characteristics. This has opened its potential deployment opportunities in versatile critical applications like the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. All these precise, complicated, and repeatable motion applications require micro and nano-scale movement control in 3D space; a 6-DOF PKM can take this challenge smartly. For this, the PKM must be more accurate than the desired application accuracy level and thus proper calibration for a PKM robot is essential. Forward kinematics-based calibration for such hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To analyze different techniques, an external instrument-based, constraint-based, and auto or self-calibration-based approaches have been used for calibration. This survey has been done by reviewing these key methodologies, their outcome, and important points related to inverse kinematic-based PKM calibrations in general. It is observed in this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by a single source or multiple sources. The error sources considered are mainly structural, in some cases, environmental factors are also considered, however, these calibrations are done under no-load conditions. This study aims to understand the current state of the art in this field and to expand the scope for other researchers in further exploration in a specific area.

This paper presents the design, development and testing of GiAnt, an affordable hexapod which is inspired by the efficient motions of ants. The decision to model GiAnt after ants rather than other insects is rooted in ants' natural adaptability to a variety of terrains. This bio-inspired approach gives it a significant advantage in outdoor applications, offering terrain flexibility along with efficient energy use. It features a lightweight 3D-printed and laser cut structure weighing 1.75 kg with dimensions of 310 mm x 200 mm x 120 mm. Its legs have been designed with a simple Single Degree of Freedom (DOF) using a link and crank mechanism. It is great for conquering challenging terrains such as grass, rocks, and steep surfaces. Unlike traditional robots using four wheels for motion, its legged design gives superior adaptability to uneven and rough surfaces. GiAnt's control system is built on Arduino, allowing manual operation. An effective way of controlling the legs of GiAnt was achieved by gait analysis. It can move up to 8 cm of height easily with its advanced leg positioning system. Furthermore, equipped with machine learning and image processing technology, it can identify 81 different objects in a live monitoring system. It represents a significant step towards creating accessible hexapod robots for research, exploration, and surveying, offering unique advantages in adaptability and control simplicity.

Legged locomotion enables robotic systems to traverse extremely challenging terrains. In many real-world scenarios, the terrain is not that difficult and these mixed terrain types introduce the need for flexible use of different walking strategies to achieve mission goals in a fast, reliable, and energy-efficient way. Six-legged robots have a high degree of flexibility and inherent stability that aids them in traversing even some of the most difficult terrains, such as collapsed buildings. However, their lack of fast walking gaits for easier surfaces is one reason why they are not commonly applied in these scenarios. This work presents LAURON VI, a six-legged robot platform for research on dynamic walking gaits as well as on autonomy for complex field missions. The robot's 18 series elastic joint actuators offer high-frequency interfaces for Cartesian impedance and pure torque control. We have designed, implemented, and compared three control approaches: kinematic-based, model-predictive, and reinforcement-learned controllers. The robot hardware and the different control approaches were extensively tested in a lab environment as well as on a Mars analog mission. The introduction of fast locomotion strategies for LAURON VI makes six-legged robots vastly more suitable for a wide range of real-world applications.

This article presents a collaborative research effort aimed at developing a novel six-degree-of-freedom (6-DOF) motion platform for the empirical characterization of hydrodynamic forces crucial for the control and stability of surface and subsurface vehicles. Traditional experimental methods, such as the Planar Motion Mechanism (PMM), are limited by the number of simultaneously articulated DOFs and are limited to single-frequency testing, making such systems impractical for resolving frequency-dependent added mass or damping matrices. The 6 DOF platform, termed a hexapod, overcomes these limitations by offering enhanced maneuverability and the ability to test broad-banded frequency spectra in multiple degrees of freedom in a single experiment.

V ersatile Locomotion Skills for Hexapod Robots Tomson Qu 1, Dichen Li 1, Avideh Zakhor 1, Wenhao Y u 2, Tingnan Zhang 2 Abstract -- Hexapod robots are potentially suitable for carrying out tasks in cluttered environments since they are stable, compact, and light weight. They also have multi-joint legs and variable height bodies that make them good candidates for tasks such as stairs climbing and squeezing under objects in a typical home environment or an attic. Expanding on our previous work on joist climbing in attics, we train a legged hexapod equipped with a depth camera and visual inertial odometry (VIO) to perform three tasks: climbing stairs, avoiding obstacles, and squeezing under obstacles such as a table. Our policies are trained with simulation data only and can be deployed on low-cost hardware not requiring real-time joint state feedback. We train our model in a teacher-student model with 2 phases: In phase 1, we use reinforcement learning with access to privileged information such as height maps and joint feedback. In phase 2, we use supervised learning to distill the model into one with access to only onboard observations, consisting of egocentric depth images and robot pose captured by a tracking VIO camera. By manipulating available privileged information, constructing simulation terrains, and refining reward functions during phase 1 training, we are able to train the robots with skills that are robust in non-ideal physical environments. We demonstrate successful sim-to-real transfer and achieve high success rates across all three tasks in physical experiments.

Abstract-- We present an integrated UAV-hexapod robotic system designed for GNSS-denied maritime operations, capable of autonomous deployment and retrieval of a hexapod robot via a winch mechanism installed on a UAV. This system is intended to address the challenges of localization, control, and mobility in dynamic maritime environments. Experimental results demonstrate the effectiveness of this system in real-world scenarios, validating its performance during field tests in both controlled and operational conditions in the MBZIRC 2023 Maritime Challenge. I. INTRODUCTION Unmanned Aerial Vehicles (UAVs) have become an essential component of modern robotics, widely used in various applications, including surveillance, inspection, search and Figure 1: UAV-Hexapod system executing its mission in a rescue, and transportation. Their ability to fly over challenging GNSS-denied maritime environment. Team KAIST won 2nd terrains and access remote areas has expanded the place in the MBZIRC 2023 Maritime Challenge.

Contact planning is crucial in locomoting systems.Specifically, appropriate contact planning can enable versatile behaviors (e.g., sidewinding in limbless locomotors) and facilitate speed-dependent gait transitions (e.g., walk-trot-gallop in quadrupedal locomotors). The challenges of contact planning include determining not only the sequence by which contact is made and broken between the locomotor and the environments, but also the sequence of internal shape changes (e.g., body bending and limb shoulder joint oscillation). Most state-of-art contact planning algorithms focused on conventional robots (e.g.biped and quadruped) and conventional tasks (e.g. forward locomotion), and there is a lack of study on general contact planning in multi-legged robots. In this paper, we show that using geometric mechanics framework, we can obtain the global optimal contact sequence given the internal shape changes sequence. Therefore, we simplify the contact planning problem to a graph optimization problem to identify the internal shape changes. Taking advantages of the spatio-temporal symmetry in locomotion, we map the graph optimization problem to special cases of spin models, which allows us to obtain the global optima in polynomial time. We apply our approach to develop new forward and sidewinding behaviors in a hexapod and a 12-legged centipede. We verify our predictions using numerical and robophysical models, and obtain novel and effective locomotion behaviors.

Abstract--The quest for the efficient adaptation of multilegged robotic systems to changing conditions is expected to render new insights into robotic control and locomotion. In this paper, we study the performance frontiers of the enumerative (factorial) encoding of hexapod gaits for fast recovery to conditions of leg failures. Our computational studies using five nature-inspired gradient-free optimization heuristics have shown that it is possible to render feasible recovery gait strategies that achieve minimal deviation to desired locomotion directives with a few evaluations (trials). For instance, it is possible to generate viable recovery gait strategies reaching 2.5 cm. Our results are the potential to enable efficient adaptation to new conditions and to explore further the canonical representations for adaptation in robotic locomotion problems.