Trot Gait Research Articles

A compliant control method for robust trot motion of hydraulic actuated quadruped robot

A motion control approach is proposed for hydraulic actuated quadruped robots, aiming to achieve active compliance and robust motion control. The approach is designed with a structure of three layers. Servo valve-controlled asymmetric hydraulic cylinder model is established to obtain the relationship between the desired torque and the control current signal, which is the bottom layer. The middle layer is based on the virtual model of the leg for active compliance. The upper layer considers the torso posture and velocity into planning the foot trajectories based on the spring loaded inverted pendulum model. Trotting gait simulations are conducted based on the proposed framework in the simulation software environment Webots. The motion control approach has been implemented on a robot prototype SCalf-II (SDU calf), where experiments have been conducted including omnidirectional trotting gait, lateral impact recovery and climbing slopes. The experiments demonstrate that the proposed approach can effectively control the hydraulic actuated robots.

Pressure Mat Analysis of Walk and Trot Gait Characteristics in 66 Normal Small, Medium, Large, and Giant Breed Dogs.

Objectives: To document temporospatial variables and gait symmetry measured by the GAITRite® system for normal, healthy dogs at the walk and trot with the leash side recorded.Study Design: Observational, prospective, cohort study.Sample Population: 66 healthy dogs of various common breeds with no evidence of lameness that were small (< 10 kg), medium (10- < 25 kg), large (25- < 40 kg), or giant (≥40 kg).Methods: Dogs walked and trotted at their preferred velocity on a pressure sensing walkway system. Video observation confirmed inclusion criteria were met for three valid trials at each gait for each dog. Coefficients of variance were used to summarize the data for analysis. Fore and hindlimb ratios were compared. Gait symmetry was assessed with the leash on the left and right side.Results: Coefficients of variation for gait parameters ranged from 20 to 28% for all except velocity and hind reach. There was no statistically significant difference in differences in fore and hindlimb ratios for stance %, GLS, TPI, or step:stride ratio, across weight categories or between walk and trot. Less than 8% of normal dogs had a GLS score < 90 (indicating lameness). Leash side did influence gait symmetry, since GLS, TPI, and step:stride all had statistically significant differences in means between leash side, irrelevant of the weight category or gait.Conclusions and Clinical Relevance: This system allowed simple, reliable gait assessment and values reported may be considered normal reference ranges for temporospatial variables collected with this system within the weight ranges and gaits reported. Controlling leash side and patient size is recommended for therapeutic intervention studies.

Selection on the Colombian paso horse's gaits has produced kinematic differences partly explained by the DMRT3 gene.

The Colombian paso horse, the most important horse breed in Colombia, performs specific and particular gaits (paso fino, trocha, and Colombian trot), which display different footfall patterns and stride frequencies. The breed has been selected for gait and conformation for more than 50 years and we hypothesize that this selection has led to kinematic differences of the gaits that can be explained by different genetic variants. Hence, the aims of the study were: 1. To identify if there are any differences in the kinematic and genetic variants between the Colombian paso horse’s gaits. 2. To evaluate if and how much the gait differences were explained by the nonsense mutation in the DMRT3 gene and 3. To evaluate these results for selecting and controlling the horses gait performance. To test our hypotheses, kinematic data, microsatellites and DMRT3 genotypes for 187 Colombian paso horses were analyzed. The results indicated that there are significant kinematic and DMRT3 differences between the Colombian paso horse’s gaits, and those parameters can be used partially to select and control the horses gait performance. However, the DMRT3 gene does not play a major role in controlling the trocha and the Colombian trot gaits. Therefore, modifying genes likely influence these gaits. This study may serve as a foundation for implementing a genetic selection program in the Colombian paso horse and future gene discovery studies for locomotion pattern in horses.

Compliant universal grippers as adaptive feet in legged robots

ABSTRACTThis work investigates the usage of compliant universal grippers as a novel foot design for legged locomotion. The method of jamming of granular media in the universal grippers is characterized by having two distinct states: a soft, fluid-like state which in locomotion can be used to damp impact forces and enable passive shape adaptation especially on rough terrain, and a hard, solid-like state that is more suited to transmit propulsion forces. We propose a system that actively uses and switches between both states of a foot design based on granular jamming and detail the implementation on a quadruped robotic platform. The mechanism is inspired by the stiffness varying function of the tarsal bones in a human foot, and our aim is to understand how the change of foot stiffness can be used to improve the locomotion performance of legged robots. Using the same open loop trot gait in all experiments, it is shown that a fast state transition enables the robot to profit from both states, leading to more uniform foot placement patterns also on rough terrain compared to other tested feet. This results in overall faster gaits and even enables the robot to climb steeper inclined surfaces.

Multi-objective Hierarchical Optimal Control for Quadruped Rescue Robot

Timely and efficient rescue missions in disasters such as nuclear accidents, fires, and earthquakes require operating robots to work under high payload. This paper treats the problem of optimal planning and control of a walking-trot gait for a hydraulically actuated quadruped robot that has been developed in a collaborative project of the Departments of Mechanical Engineering and Automation at Shanghai Jiao Tong University. To mitigate the challenges of working with high-fidelity models of this highly complex mechanical system, a kinematics and approximate dynamics model is proposed that is shown to provide an accurate description of the walking motions we wish to study while at the same time being simple enough to support analysis. The proposed model is used to design limb movements in a walking trot gait that balance the trade off between energy consumption and the speed of execution of a desired mission. Bezier curves of different orders are used to design trajectories of the robot’s limbs. We verify the accuracy of the proposed model through experiments with the actual robot. We apply hierarchical optimization method to minimize the energy consumption, and we discuss a Pareto optimal solution that trades off mission duration and energy consumption. In the end perform several experiments to verify the effectiveness and superiority of the optimal algorithm we proposed.

Towards dynamic alternating tripod trotting of a pony-sized hexapod robot for disaster rescuing based on multi-modal impedance control

SUMMARYHexapod robots are well suited for disaster rescuing tasks due to their stability and load capability. However, most current hexapod robots still rely on static gaits that largely limit their locomotion speed. This paper introduces a hierarchical control strategy to realize a dynamic alternating tripod trotting gait for a hexapod robot based on multi-modal impedance control. At the low level, a position-based impedance controller is developed to realize an adjustable compliant behavior for each leg. At the high level, a new gait controller is developed to generate a stable alternating tripod trotting gait, in which a gait state machine, a leg compliance modulation strategy, and a close-looped body attitude stabilizer are imposed. As a result, the alternating tripod trotting of the hexapod robot can be synchronized as the running of a bipedal robot with stable body attitude. Moreover, this control strategy was verified by experiments on a newly designed pony-sized disaster rescuing robot, HexbotIV, which successfully achieved a dynamic trotting gait with ability to resist the disturbances of mildly uneven terrains. Our control strategy as well as the experimental study can be a valuable reference for other hexapod robots and thus paves a way to the practical deployment of disaster rescuing robots.

Foot Trajectory Planning and Optimization Simulation of Low Foot-Terrain Impact by Quadruped Robot Based on the Trot Gait

In this essay, I design a bionic quadruped robot driven by a large torque electric cylinder, and establish a kinematics model of it by coordinate transformation. Then I analyze the phase relationship between the one-legged wobble and the supporting phase. For the Trot gait of bionics quadruped robot, an improved algorithm of foot trajectory planning with low force and low energy consumption is proposed. In the gait planning, with the help of kinematic inverse kinematics, the joint function of the leg is solved and the control function of the telescoping capacity of the electric cylinder is deduced by geometric relationship. In MATLAB environment, I simulate and analyze the gait and energy consumption, and carry out the servo control of each leg of the experimental prototype to realize the walking of Trot gait robot with bionic quadruped robot. The simulation results show that the trajectory planning can achieve the continuous and steady walking of the bionic quadruped robot driven by the electric cylinder. Moreover, the trajectory of the foot is smooth, the torso is small, which proves the effectiveness and rationality of the method.

The Gait Design and Trajectory Planning of a Gecko-Inspired Climbing Robot.

Inspired by the dynamic gait adopted by gecko, we had put forward GPL (Gecko-inspired mechanism with a Pendular waist and Linear legs) model with one passive waist and four active linear legs. To further develop dynamic gait and reduce energy consumption of climbing robot based on the GPL model, the gait design and trajectory planning are addressed in this paper. According to kinematics and dynamics of GPL, the trot gait and continuity analysis are executed. The effects of structural parameters on the supporting forces are analyzed. Moreover, the trajectory of the waist is optimized based on system energy consumption. Finally, a bioinspired robot is developed and the prototype experiment results show that the larger body length ratio, a certain elasticity of the waist joint, and the optimized trajectory contribute to a decrease in the supporting forces and reduction in system energy consumption, especially negative forces on supporting feet. Further, the results in our experiments partly explain the reasonability of quadruped reptile's kinesiology during dynamic gait.

The Mathematical Modeling and Dynamic Trot Gait Simulation on the Single Leg Hydraulic Drive System of the Quadruped Robot

In this paper, the single leg hydraulic drive system of the quadruped robot is taken as the research object. Then the nonlinear mathematical model of the hydraulic system is built. According to the real mechanical structure parameters of the single leg, the relationship between position control characteristics of the system and variation of single leg trajectory is investigated. Besides, the tracing accuracy of single leg foot displacement in one trot gait condition is analyzed through combination of kinematics solution and simulation analysis. In conclusion, the research indicates that the nonlinear mathematical model can be used to analyze the position control performance of the single leg hydraulic drive system. This research provides a basic foundation for further research of control method.

未知の斜面における4脚歩行ロボットのZMPに基づくトロット歩容

We focus on a quadruped robot as a mobile platform which would work at various environment such as disaster sites, offices and factories. In this paper, we assume that terrain consists of slopes and we propose a walking gait for a quadruped robot on unknown slopes. In this method, the robot basically walks in trot gait because trot gait has both high stability and practical walking speed in order to walk stably on steep slopes. At first, robot estimates slant of the slope by using body attitude and foot positions on the slope. Then it generates walking pattern for the robot to walk stably on the slope by using inverted pendulum model and multi-mass model of the robot. The proposed method was verified through experiments with a quadruped robot TITAN-VIII walked on slopes where a step or other slope exist halfway.

生物の神経構造と筋骨格を模した4脚動物モデルによる歩容遷移現象の創発

This study aims to understand the principles of gait (the order of the movement of four legs) transition phenomenon in quadrupedal animals. Each of a quadruped animal's gaits are considered to be generated by neural networks placed in the spinal cord. Furthermore, the gait is changed according to its speed. However, the mechanism of gait transition is still unrevealed. To reveal it, we built a simulated quadruped model which is equipped with a cat's musculoskeletal system and nervous system that consists of central pattern generators (CPGs) and sensory afferent feedbacks. The model safely locomoted with a trot gait at a variety of speeds. We aim to allow the model to walk with leg load feedbacks.

4足歩行ロボットのための位置指定揺動型間歇トロット歩容

For a quadruped robot, the crawl gait is commonly used on rough terrain environment where a pre-motion planing is required. However its walking speed is slower than other walking gaits and make it difficult to develop a practical legged robot. Among the various types of gaits, we consider that the trot gait is safety gait which can prevent complete falling by hitting its swinging leg on the ground. Therefore in this paper we propose a position specified sway compensation trajectory based on 3D sway compensation trajectory which can control footsteps and end position of the center of gravity to walk over rough terrain environment. The validity of the proposed algorithm is confirmed by using physics simulator V-REP with model of experimental quadruped robot TITAN-XIII. As a result, the robot model succeeded to walk over simple step, and random step and proved the feasibility of the proposed gait on a difficult terrain.

四脚歩行ロボットのトロット歩容における目標位置への最短時間制御

A design method of time-optimal trajectory of quadruped robots from an initial position to a target position is developed for trot gait. The designed trajectory consists of three phases, acceleration phase, steady walk phase and deceleration phase. The time-optimal trajectory is designed in each phase and they are integrated so that the robot reaches the target position. Since the fastest walk trajectory in steady walk has already been obtained in our previous research, the time-optimal trajectories in the acceleration and deceleration phases are designed in a similar way to the previous study. First, all the possible trajectories in the search space with which the velocity of the robot reaches the previously obtained maximum velocity are designed in the state space of the robot. Next, they are checked whether the physical constraints and the constraint imposed by swinging legs are satisfied or not. Then the trajectory with the shortest time to reach the maximum velocity is chosen as the time-optimal trajectory among the trajectories satisfying all the constraints. The obtained time-optimal trajectories are tested by a quadruped walking robot SONY ERS-7 and the effectiveness of the developed method of designing time-optimal trajectory is verified.

Gait analysis of goat at different slopes and study on biomimetic walking mechanism

To study the walking status of a goat on slope and the walking mechanics, a comparative analysis of the walking gait mode of a goat on different slopes was conducted. The uphill and downhill walking processes on different slopes (6°, 18° and 36°) were recorded by a high speed video system. The experimental image results were processed and analyzed via SigmaScan software and MATLAB software. The characteristic parameters of locomotion gait on the different slopes and the angle change curves of each goat leg in the process of slope movement indicated that the goat performed tetrapod gait, static gait, ipsilateral gait and trot gait on different slopes. With the increase of gradient in the uphill process, the corresponding load factors of each leg were 0.65±0.15, 0.75 and 0.645±0.205, whereas those in the downhill process were 0.70±0.08, 0.66±0.06, and 0.685±0.125. Results showed that the load factors of each leg are higher than 0.5. The foreleg angle of  (the angle of wrist joints), which ranges from 100° to 130°, is suitable for different slopes. However, the angle of  (the angle between the thigh and the forward direction in the walking process of goat), which ranges from 99° to 109°, is suitable for the 6° slope, whereas the angle ranging from 46° to 91° is suitable for the 18° slope and 36° slope. For the hind leg, the angle of , which ranges from 105° to 153°, is suitable for the different slopes. The angle of , which ranges from 128° to 150°, is suitable for the different slopes. The research can provide a theoretical basis and experimental data for the design of biomimetic agricultural slope walking mechanism. Keywords: biomimetic walking, goat gait, slope walking mechanism, agricultural robot, SigmaScan, MATLAB DOI: 10.3965/j.ijabe.20160903.2260 Citation: Zhang F, Wang W, Zhang G Y, Wang J, Qiu Z M, Mao P J. Gait analysis of goat at different slopes and study on biomimetic walking mechanism. Int J Agric & Biol Eng, 2016; 9(3): 40－47.

強化学習に基づく4脚走行ロボットのトロット歩容獲得と動作改善

When we develop robots, we cannot completely deal with unexpected situations and unknown environments in advance. One way to solve this problem is reinforcement learning, which is a technique for finding an optimal behavior pattern with respect to the target depending on the circumstances and environment through trial and error. This learning enables an action suitable for the achievement of the aim tailored to the environment without changing the control program. However, it takes a lot of time to complete learning. In this study, we applied reinforcement learning to our four-legged robot modeled on four-legged animals and examined whether the robot could acquire an improved trotting gait. As a result, the robot acquired the trotting gait. Furthermore, in repeated learning, running speed became 31% faster, and energy consumed fell by 23% because running movement was improved.

Co-simulation of a quadruped robot's mechanical and hydraulic systems based on ADAMS and AMESim

In order to observe the change and fluctuation in flow and pressure of a hydraulic quadruped robot's hydraulic system when the robot walks on trot gait, a co-simulation method based on ADAMS and AMESim is proposed. Firstly, the change rule in each swing angle of the hydraulic quadruped robot's four legs is analyzed and converted to the displacement change of the hydraulic cylinder by calculating their geometric relationship. Secondly, the robot's dynamic model is built in ADAMS and its hydraulic and control system models are built in AMESim. The displacement change of the hydraulic cylinder in the hydraulic system is used as the driving function of the dynamics model in ADAMS, and the driving force of the dynamics model is used as the loads of the hydraulic system in AMESim. By introducing the PID closed-loop control in the control system, the co-simulation between hydraulic system and mechanical system is implemented. Finally, the curve of hydraulic cylinders' loads, flow and pressure are analyzed and the results show that they fluctuate highly in accordance with the real situation. The study provides data support for the development of a hydraulic quadruped robot's physical prototype.

脚関節トルクの冗長性を利用した四脚ロボットのトロット歩容における最速歩行制御

A way of deriving the fastest walk pattern of quadruped robots for trot gait is developed and installed into a practical robot system. Two support legs and the body are modeled as a five-link manipulator and each swinging leg is modeled as a two link manipulator respectively. As a first step, the fastest walk pattern of support legs is designed under the constraints of torque limits of leg joints and friction forces at the support leg tips. Then, the time optimal motion pattern of each swing leg is designed under the boundary conditions given by the obtained walk pattern of the support legs. The fastest walk patterns of support legs and swinging legs are designed respectively. Therefore, if the time optimal motion pattern of swinging legs doesn't satisfy the boundary conditions given by support legs, the same procedures are iterated by modifying a velocity parameter of the support legs until the boundary conditions are satisfied. SONY ERS-7 is used as a quadruped walking robot and some fundamental experiments are done to verify the effectiveness of the developed control algorithm. From the results, it is revealed that the proposed method is particularly effective on the ground with large friction coefficients.

A biologically based neural system coordinates the joints and legs of a tetrapod

A biologically inspired neural control system has been developed that coordinates a tetrapod trotting gait in the sagittal plane. The developed neuromechanical system is used to explore properties of connections in inter-leg and intra-leg coordination. The neural controller is built with biologically based neurons and synapses, and connections are based on data from literature where available. It is applied to a planar biomechanical model of a rat with 14 joints, each actuated by a pair of antagonistic Hill muscle models. The controller generates tension in the muscles through activation of simulated motoneurons. The hind leg and inter-leg control networks are based on pathways discovered in cat research tuned to the kinematic motions of a rat. The foreleg network was developed by extrapolating analogous pathways from the hind legs. The formulated intra-leg and inter-leg networks properly coordinate the joints and produce motions similar to those of a walking rat. Changing the strength of a single inter-leg connection is sufficient to account for differences in phase timing in different trotting rats.

Assessment of the Stability of a Four Legged Robot Manipulator

This paper deals with static stability of a four legged robot manipulator when it moves with trot gait. In this paper, the stability analysis based on dynamics of walking usually proposed for the analysis of walking system studied and identified its limits and ambiguity. After identifying the key issues of stability, it has been identified that moment around the supporting diagonal line of quadruped in trotting gait largely influences walking stability. Therefore Moment around the supporting diagonal line of quadruped in trotting gait is modeled and its effects on body attitude (roll and pitch) are analyzed. The degree of influence varies with different initial stances of quadruped and we get the optimal initial stance of quadruped in trotting gait with maximal walking stability. Simulation results are presented.

A gait transition algorithm based on hybrid walking gait for a quadruped walking robot

This paper presents a quasi-dynamic gait, called Hybrid Walking Gait, and a new gait transition algorithm for a quadruped walking robot. The Hybrid Walking gait reduces the steps of a generic walking gait with primitive foot trajectory generation using some of parameters easily defined. It shows great improvements over existing ones in terms of higher mobility, less complexity to define the motion, and smooth body movements that affect to the stability of the robot. The Gait Transition pattern generated with the Hybrid Walking Gait guarantees stability as good as that of a traditional walking gait and high mobility such as the dynamic trot gait. We perform experiments with a quadruped robot called "Artificial Digitigrade for Natural Environments Version III", and validate the effectiveness of our proposed gait patterns over several types of terrains.