Trot Gait Research Articles

A composite motion control method for quadruped robots in trot gait

This work aims to address the issues of instability in trot gait walking and poor terrain adaptability in rugged environments under conventional control strategies for quadruped robots by proposing a novel composite control strategy. During the support phase, a separated force-position mixing control method is employed, utilizing gravity-compensated PD (Proportional Derivative) control at the lateral swing and knee joints while employing position control at the hip joint. During the swing phase, VMC (Virtual Model Control) is used to construct three sets of virtual spring-damper components, guiding the foot to move along a predetermined trajectory and converting virtual forces into joint torques for the swinging leg. At the body, IMU (Inertial Measurement Unit) feedback data combined with PI (Proportional Integral) control is used to adjust leg length and maintain the robot’s posture stability. Finally, the proposed separated force-position hybrid control method is theoretically validated using the Lyapunov stability criterion, and simulation tests on flat and rugged terrains under the quadruped robot’s composite control method are conducted using MATLAB/Simulink, comparing it with the VMC and position control methods. The findings indicate that the composite control strategy leads to smaller changes in the attitude angles and reduced impact forces at the feet during the quadruped robot’s walk on flat ground while also demonstrating strong adaptability to rugged terrains.

A neural network model for goat gait.

In this paper, our main objective was to investigate the central pattern generator (CPG) neural network model for quadruped gait with time delay. First, we computed the normal form of the model on the center manifold, the bifurcation direction, and stability conditions of the bifurcating periodic solutions. Second, we applied the CPG model for quadruped gait to obtain reference models for goat's diagonal trotting gait on the flat ground and walking gait on the 18 degree slope through the trust region inversion algorithm. Finally, we performed numerical simulations to support theoretical analysis.

Wall-climbing performance of gecko-inspired robot with soft feet and digits enhanced by gravity compensation

Gravitational forces can induce deviations in body posture from desired configurations in multi-legged arboreal robot locomotion with low leg stiffness, affecting the contact angle between the swing leg’s end-effector and the climbing surface during the gait cycle. The relationship between desired and actual foot positions is investigated here in a leg-stiffness-enhanced model under external forces, focusing on the challenge of unreliable end-effector attachment on climbing surfaces in such robots. Inspired by the difference in ceiling attachment postures of dead and living geckos, feedforward compensation of the stance phase legs is the key to solving this problem. A feedforward gravity compensation (FGC) strategy, complemented by leg coordination, is proposed to correct gravity-influenced body posture and improve adhesion stability by reducing body inclination. The efficacy of this strategy is validated using a quadrupedal climbing robot, EF-I, as the experimental platform. Experimental validation on an inverted surface (ceiling walking) highlights the benefits of the FGC strategy, demonstrating its role in enhancing stability and ensuring reliable end-effector attachment without external assistance. In the experiment, robots without FGC only completed 3 out of 10 trials, while robots with FGC achieved a 100% success rate in the same trials. The speed was substantially greater with FGC, achieving 9.2 mm s−1 in the trot gait. This underscores the proposed potential of the FGC strategy in overcoming the challenges associated with inconsistent end-effector attachment in robots with low leg stiffness, thereby facilitating stable locomotion even at an inverted body attitude.

A Unified Motion Generation Approach for Quadruped L-S Walk and Trot Gaits Based on Linear Model Predictive Control

A Unified Motion Generation Approach for Quadruped L-S Walk and Trot Gaits Based on Linear Model Predictive Control

An Untethered Soft Robotic Dog Standing and Fast Trotting with Jointless and Resilient Soft Legs.

Soft robots are compliant, impact resistant, and relatively safe in comparison to hard robots. However, the development of untethered soft robots is still a major challenge because soft legs cannot effectively support the power and control systems. Most untethered soft robots apply a crawling or walking gait, which limits their locomotion speed and mobility. This paper presents an untethered soft robot that can move with a bioinspired dynamic trotting gait. The robot is driven by inflatable soft legs designed on the basis of the pre-charged pneumatic (PCP) actuation principle. Experimental results demonstrate that the developed robot can trot stably with the fastest speed of 23 cm/s (0.97 body length per second) and can trot over different terrains (slope, step, rough terrain, and natural terrains). The robotic dog can hold up to a 5.5 kg load in the static state and can carry up to 1.5 kg in the trotting state. Without any rigid components inside the legs, the developed robotic dog exhibits resistance to large impacts, i.e., after withstanding a 73 kg adult (46 times its body mass), the robotic dog can stand up and continue its trotting gait. This innovative robotic system has great potential in equipment inspection, field exploration, and disaster rescue.

Multi-constraint spatial coupling for the body joint quadruped robot and the CPG control method on rough terrain

Quadruped robots have frequently appeared in various situations, including wilderness rescue, planetary exploration, and nuclear power facility maintenance. The quadruped robot with an active body joint has better environmental adaptability than one without body joints. However, it is difficult to guarantee the stability of the body joint quadruped robot when walking on rough terrain. Given the above issues, this paper proposed a gait control method for the body joint quadruped robot based on multi-constraint spatial coupling (MCSC) algorithm. The body workspace of the robot is divided into three subspaces, which are solved for different gaits, and then coupled to obtain the stable workspace of the body. A multi-layer central pattern generator model based on the Hopf oscillator is built to realize the generation and switching of walk and trot gaits. Then, combined with the MCSC area of the body, the reflex adjustment strategy on different terrains is established to adjust the body’s posture in real time and realize the robot’s stable locomotion. Finally, the robot prototype is developed to verify the effectiveness of the control method. The simulation and experiment results show that the proposed method can reduce the offset of the swing legs and the fluctuation of the body attitude angle. Furthermore, the quadruped robot is ensured to maintain stability by dynamically modifying its body posture. The relevant result can offer a helpful reference for the control of quadruped robots in complex environments.

A randomized, triple-blinded controlled clinical study with a novel disease-modifying drug combination in equine lameness-associated osteoarthritis

ObjectiveThis study aimed to test a novel treatment combination (TC) (equivalent to sildenafil, mepivacaine, and glucose) with disease-modifying properties compared to Celestone® bifas® (CB) in a randomized triple-blinded phase III clinical study in horses with mild osteoarthritis (OA). Joint biomarkers (reflecting the articular cartilage and subchondral bone remodelling) and clinical lameness were used as readouts to evaluate the treatment efficacy. MethodsTwenty horses with OA-associated lameness in the carpal joint were included in the study and received either TC (n = 10) or CB (n = 10) drug intra-articularly-twice in the middle carpal joint with an interval of 2 weeks (visit 1 & 2). Clinical lameness was assessed both objectively (Lameness locator) and subjectively (visually). Synovial fluid and serum were sampled for quantification of the extracellular matrix (ECM) neo-epitope joint biomarkers represented by biglycan (BGN262) and cartilage oligomeric matrix protein (COMP156). Another two weeks later clinical lameness was recorded, and serum was collected for biomarkers analysis. The overall health status was compared pre and post-intervention by interviewing the trainer. ResultsPost-intervention, SF BGN262 levels significantly declined in TC (P = 0.002) and COMP156 levels significantly increased in CB (P = 0.002). The flexion test scores improved in the TC compared to CB (P =0.033) and also had an improved trotting gait quality (P =0.044). No adverse events were reported. ConclusionThis is the first clinical study presenting companion diagnostics assisting in identifying OA phenotype and evaluating the efficacy and safety of a novel disease-modifying osteoarthritic drug.

Comparison Between Trot and Wave Gait Applied in Quadruped Robot

A Quadruped robot is a type of robot that moves on four legs and has a structure like a four-legged animal. The quality of movement based on mechanics and movement patterns on quadruped robots tends to have poor movement patterns. This study investigates the best movement between trot and wave gait by comparing the speed performance, stopping distance accuracy, and the tilt of the robot body angle. To minimize the influence of the mechanical quality of the robot, this study used two robots based on the type of servo used (based on the SG90 and MG995 servos). In this study, the motion pattern based on Trot and Wave gait is realized using Inverse Kinematics and Polynomial trajectory on each leg. The verification experiment showed that the Wave gait has better in both the robot body angle and distance error. In contrast the Trot gait has better in speed.

A Simple Controller for Omnidirectional Trotting of Quadrupedal Robots: Command Following and Waypoint Tracking

For autonomous legged robots to be deployed in practical scenarios, they need to perform perception, motion planning, and locomotion control. Since robots have limited computing capabilities, it is important to realize locomotion control with simple controllers that have modest calculations. The goal of this paper is to create computational simple controllers for locomotion control that can free up computational resources for more demanding computational tasks, such as perception and motion planning. The controller consists of a leg scheduler for sequencing a trot gait with a fixed step time; a reference trajectory generator for the feet in the Cartesian space, which is then mapped to the joint space using an analytical inverse; and a joint controller using a combination of feedforward torques based on static equilibrium and feedback torque. The resulting controller enables velocity command following in the forward, sideways, and turning directions. With these three velocity command following-modes, a waypoint tracking controller is developed that can track a curve in global coordinates using feedback linearization. The command following and waypoint tracking controllers are demonstrated in simulation and on hardware.

Trot Gait Stability Control of Small Quadruped Robot Based on MPC and ZMP Methods

The stability of a quadruped robot is mainly affected by the obstacles in the horizontal direction and the roughness in the vertical direction, which often leads to the robot unable to achieve the desired gait effect. In order to solve this problem, the Model Predictive Control (MPC) model and the Zero Moment Point (ZMP) method are combined, and applied to gait planning and the foot end landing control of a small quadruped robot. The tort gait of a small quadruped robot is the focus of research in this study, which simulated trajectory planning and gait stability. In addition, through comparative analysis with the corresponding experiments, the results show that the simulation results are similar to the experimental results, and the quadruped robot gait is stable. Meanwhile, it shows that the combination of the MPC model and ZMP method is feasible for gait stability control of a quadruped robot.

Torque Simulation and Analysis of Quadruped Robot under Trot Gait

The quadruped robot can overcome the unevenness of the wheeled chassis on steps and gravel roads, and has good passability. The Trot gait is the basic gait of the quadruped robot, and the walking is realized by the gait of alternating footsteps. In this paper, the dynamic simulation of the static equilibrium state of the quadruped robot in different poses on the ground and stair is carried out, and the movement of the robot body under the trot gait is simulated to obtain the joint torques of the upper and lower leg of the quadruped robot, which is the driving torque of the joint motor. The model selection provides a theoretical basis, and at the same time, the motion analysis of the quadruped robot is carried out, and the moving distance of the chassis under the extreme posture is planned.

Cooperative control strategy of wheel-legged robot based on attitude balance

AbstractTo integrate the uneven terrain adaptivity of legged robots and the fast capacity of wheeled robots on even terrains, a four wheel-legged robot is addressed and the cooperative control strategy of wheels and legs based on attitude balance is investigated. Firstly, the kinematics of wheel-legged robot is analyzed, which contains the legged and wheeled motion modal. Secondly, the cooperative control strategy of wheel-legged robot based on attitude balance is proposed. The attitude is calculated by using the quaternion method and complementary filtering, and the attitude stability control of the wheel-legged robot is studied. The trajectory planning of leg motion including walk and trot gait is implemented, and the differential control of wheeled motion is deduced. And then, the cooperative motion control of wheels and legs is achieved by keeping the attitude balance of robot body. Finally, a small prototype is set up to validate the feasibility and effectiveness of proposed method. The experimental results show that the established wheel-legged robot can do walk, trot, and wheel-leg compound motion to overcome many complex terrains and environments.

Wearable Inertial Sensor-Based Limb Lameness Detection and Pose Estimation for Horses

Accurate objective, automated limb lameness detection and pose estimation play an important role for animal well-being and precision livestock farming. We present a wearable sensor-based limb lameness detection and pose estimation for horse walk and trot locomotion. The gait event and lameness detection are first built on a recurrent neural network (RNN) with long short-term memory (LSTM) cells. Its outcomes are used in the limb pose estimation. A learned low-dimensional motion manifold is parameterized by a phase variable with a Gaussian process dynamic model. We compare the RNN-LSTM-based lameness detection method with a feature-based multi-layer classifier (MLC) and a multi-class classifier (MCC) that are built on support vector machine/K-nearest-neighbors and deep convolutional neural network methods, respectively. Experimental results show that using only accelerometer measurements, the RNN-LSTM-based approach achieves 95% lameness detection accuracy and also outperforms the feature-based MLC or MCC in terms of several assessment criteria. The pose estimation scheme can predict the 24 limb joint angles in the sagittal plane with average errors less than 5 and 10 degs under normal and induced lameness conditions, respectively. The presented work demonstrate the successful use of machine learning techniques for high performance lameness detection and pose estimation in equine science. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Automation technologies are increasingly used for precision agriculture but few have focused on monitoring individual animals in open field for precision livestock farming. Limb lameness detection and pose estimation in open field is labor-intensive, unsafe for farmers, and inefficient. The presented machine learning-enabled, wearable inertial sensor-based design provides an effective and efficient approach for horse limb lameness detection and pose estimation applications. We present an RNN-LSTM for lameness detection and an integrated manifold learning model is used to predict the horse limb joint angles in walk and trot gaits under normal and induced lameness conditions. We also present a systematic analysis and experiments to demonstrate the impacts of the wearable sensor locations and signal information on lameness detection and pose estimation performance. Several other machine learning-based lameness detection methods are also presented and compared. The extensive multi-horse testing results are presented to demonstrate the superior accuracy and higher performance than other types of machine learning methods. One attractive feature of the proposed design lies in its high performance and fast computational capability for potential real-time applications in open field.

Balance control based on six-dimensional spatial mechanics and velocity adjustment through region intervention and foot landing for quadruped robot

AbstractCurrently, the body balance control algorithm of a quadruped robot executing trot gait motion is more complex and computationally intensive, which is not conducive to improving the real-time control performance of the robot. This paper proposes a six-dimensional spatial mechanics decoupling algorithm to enhance the balance control accuracy during trot gait while optimizing the computational effort. A 6 × 6 matrix is established to describe the relationship between six ground reaction forces of the diagonal supporting leg and six spatial forces and torques controlling robot degrees of freedom, which is optimized to reach the full rank. Decoupling calculation is adopted to obtain required ground reaction forces by matrix inverse operation, and forces are converted to joint motor torques utilizing the Jacobian matrix. The trajectory of the swing leg foot is generated based on cubic interpolation, and the robot motion speed is adjusted by selecting the landing point. This paper also proposes a region intervention control method based on center of mass projection to regulate the moving speed while ensuring the balance of the robot. Finally, the algorithm is verified by simulation using open source software Webots. The results show that when the robot moves at an average speed of 0.5 m/s, the lateral displacement change of the robot is less than 0.009 m, the height change is less than 0.003 m, and the rotating angles around the x, y, and z axes are less than 0.0036 rad, 0.0013 rad, and 0.001 rad, respectively.

Trot gait control of a quadruped robot with elastic legs

Trot gait control of a quadruped robot with elastic legs

Whole-body kinematic and dynamic modeling for quadruped robot under different gaits and mechanism topologies.

Dynamic locomotion plays a crucial role for legged robots to fulfill tasks in unstructured environments. This paper proposes whole-body kinematic and dynamic modeling method s based on screw theory for a quadruped robot using different gaits and mechanism topologies. Unlike simplified models such as centroid or inverse pendulum models, the methods proposed here can handle 10-dimensional mass and inertia for each part. The only simplification is that foot contact models are treated as spherical joints. Models of three different mechanism topologies are formulated: (1) Standing phase: a system consisting of one end-effector, the body, and four limbs, the legs; (2) Walking phase: a system consisting of one or two lifting legs (depending on the chosen gait), two or three supporting legs; (3) Floating phase: a system in which all legs detach from the ground. Control strategies based on our models are also introduced, which includes walk and trot gait plans. In our control system, two additional types of information are provided: (1) contacting forces are given by force sensors installed under feet; (2) body poses are determined by an inertial measurement unit (IMU). Combined with the sensor data and calibrated mass, inertia, and friction, the joint torque can be estimated accurately in simulation and experiment. Our prototype, the “XiLing” robot, is built to verify the methods proposed in this paper, and the results show that the models can be solved quickly and leads to steady locomotions.

Structural Design, Simulation and Experiment of Quadruped Robot

This paper carried out a series of designs, simulations and implementations by using the physical-like mechanism of a bionic quadruped robot dog as a vehicle. Through an investigation of the walking mechanisms of quadrupeds, a bionic structure is proposed that is capable of omnidirectional movements and smooth motions. Furthermore, the kinematic and inverse kinematic solutions based on the DH method are explored to lay the foundation for the gait algorithm. Afterward, a classical compound pendulum equation is applied as the foot-end trajectory and inverse kinematic solutions are combined to complete the gait planning. With appropriate foot–ground contact modeling, MATLAB and ADAMS are used to simulate the dynamic behavior and the diagonal trot gait of the quadruped robot. Finally, the physical prototype is constructed, designed and debugged, and its performance is measured through real-world experiments. Results show that the quadruped robot is able to balance itself during trot motion, for both its pitch and roll attitude. The goal of this work is to provide an affordable yet comprehensive platform for novice researchers in the field to study the dynamics, contact modeling, gait planning and attitude control of quadruped robots.

Lateral Undulation of the Bendable Body of a Gecko-Inspired Robot for Energy-Efficient Inclined Surface Climbing

Sprawling posture animals with their bendable spine, such as salamanders, and geckos, can perform agile and versatile locomotion including walking, swimming, and climbing. Therefore, several roboticists have used them as templates for robot designs to investigate and generate efficient locomotion. Typically, walking and/or swimming abilities are realized by salamander-inspired robots with a bendable body, whereas climbing ability is achieved on gecko-inspired robots with an over-simplified fixed body. In this study, we propose optimal bendable body design with three degrees of freedom (DOFs). Its implementation on a sprawling posture robot is inspired by geckos for climbing enhancement. The robot leg and body movements are coordinated and driven by central pattern generator (CPG)-based neural control. As a consequence, the robot can climb using a combination of trot gait and lateral undulation of the bendable body with a C-shaped standing wave. Through the real robot experiments on a 3D force measuring platform, we demonstrate that, due to the dynamics of the bendable body movement, the robot can gain higher medio-lateral (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) ground reaction forces (GRFs) at its front legs as well as anterior-posterior (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> ) GRFs at its hind legs to increase the bending angular momentum (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> ). This results in 52% and 54% reduced energy consumptions during climbing on steeper inclined solid and soft surfaces, respectively, compared to climbing with a fixed body. To this end, the study provides a basis for developing sprawling posture robots with a bendable body and neural control for energy-efficient inclined surface climbing with a possible extension towards agile and versatile locomotion, such as sprawling posture animals.

A minimal robophysical model of quadriflagellate self-propulsion

Locomotion at the microscale is remarkably sophisticated. Microorganisms have evolved diverse strategies to move within highly viscous environments, using deformable, propulsion-generating appendages such as cilia and flagella to drive helical or undulatory motion. In single-celled algae, these appendages can be arranged in different ways around an approximately 10 μm long cell body, and coordinated in distinct temporal patterns. Inspired by the observation that some quadriflagellates (bearing four flagella) have an outwardly similar morphology and flagellar beat pattern, yet swim at different speeds, this study seeks to determine whether variations in swimming performance could arise solely from differences in swimming gait. Robotics approaches are particularly suited to such investigations, where the phase relationships between appendages can be readily manipulated. Here, we developed autonomous, algae-inspired robophysical models that can self-propel in a viscous fluid. These macroscopic robots (length and width = 8.5 cm, height = 2 cm) have four independently actuated ‘flagella’ (length = 13 cm) that oscillate under low-Reynolds number conditions (Re ). We tested the swimming performance of these robot models with appendages arranged two distinct configurations, and coordinated in three distinct gaits. The gaits, namely the pronk, the trot, and the gallop, correspond to gaits adopted by distinct microalgal species. When the appendages are inserted perpendicularly around a central ‘body’, the robot achieved a net performance of 0.15–0.63 body lengths per cycle, with the trot gait being the fastest. Robotic swimming performance was found to be comparable to that of the algal microswimmers across all gaits. By creating a minimal robot that can successfully reproduce cilia-inspired drag-based swimming, our work paves the way for the design of next-generation devices that have the capacity to autonomously navigate aqueous environments.

Force-based Active Compliance Control of Hydraulic Quadruped Robot

The hydraulically driven quadruped robot has received extensive attention from many scholars due to its high power density and adaptability to unstructured terrain. However, the research on hydraulic quadruped robots based on torque control is not mature enough, especially in the aspect of multi-rigid body dynamics. In this paper, the most commonly used gait trot is selected as the research object. First, the multi-rigid motion equation of the quadruped robot is established by the spin recursion method based on Lie groups. Next, the Lagrange multiplier is used to represent the constraint force to establish the 12-degree-of-freedom inverse dynamics model of the quadruped robot’s stance phase. And the hybrid dynamics method is used to reduce the dimension of the inversion matrix, which simplifies the solution process of the dynamics model. Then, the trajectory of the foot is planned. Through the analysis of the simplified model, it is concluded that the gait cycle and the initial position of the stance phase are important factors affecting the stability of the trot gait. Finally, the controller framework of the quadruped robot is introduced, and the effectiveness of the algorithm designed in this paper is verified through the co-simulation of the trot gait. The co-simulation results show that the inverse dynamics algorithm can be used as the feedforward of the control system, which can greatly reduce the gains of the PD controller; the robot has good compliance and can achieve stable trotting.