Bionic Quadruped Robot Dynamic Gait Control Strategy Based on Twenty Degrees of Freedom

Quadruped robot dynamic gaits have much more advantages than static gaits on speed and efficiency, however high speed and efficiency calls for more complex mechanical structure and complicated control algorithm. It becomes even more challenging when the robot has more degrees of freedom. As a result, most of the present researches focused on simple robot, while the researches on dynamic gaits for complex robot with more degrees of freedom are relatively limited. The paper is focusing on the dynamic gaits control for complex robot with twenty degrees of freedom for the first time. Firstly, we build a relatively complete 3D model for quadruped robot based on spring loaded inverted pendulum (SLIP) model, analyze the inverse kinematics of the model, plan the trajectory of the swing foot and analyze the hydraulic drive. Secondly, we promote the control algorithm of one-legged to the quadruped robot based on the virtual leg and plan the state variables of pace gait and bound gait. Lastly, we realize the above two kinds of dynamic gaits in ADAMS-MATLAB joint simulation platform which testify the validity of above method.      

Gait optimization of step climbing for a hexapod robot

RHex-style hexapod robot is a type of legged robot which can perform multiple moving gaits according to different applications, due to its simple structure and strong mobility. However, traversing high obstacles has always been a big challenge for legged robots. In this paper, gait optimization of a hexapod robot is proposed for climbing steps at different heights, which even enables the robot to climb the step 3.9 times of the leg length. First, a previous step-climbing gait is optimized by adjusting body inclination when placing front legs on top of the step, which enables RHex with different sizes to perform the rising stage of the gait. Second, to improve the climbing heights, a novel quasi-static climbing gait is proposed by using the reversed claw-shape legs to reach the higher step. The nondeformable legs are used to raise the center of mass (COM) of the body by lifting the front and rear legs alternately so that the front legs can reach the top of the step, then the front and middle legs are lifted alternately to maneuver COM up onto the step. The simulations and dynamic analysis of climbing steps are utilized to verify the feasibility of the improved gait. Finally, the step-climbing experiments at different heights are performed with the optimized gaits to compare with the existing gaits. The results of simulations and experiments show the superiority of the proposed gaits due to climbing higher steps.     

Development of a new spinning gait for a planar snake robot using central pattern generators

In this paper, we first present dynamic equation of n-link snake robot using Lagrange’s method in a simplified matrix form and verify them experimentally. Next, we introduce a new locomotion mode called spinning gait. Central pattern generators (CPGs) are used for online gait generation. To realize spinning gait, genetic algorithm is used to find optimal CPG network parameters. We illustrate both theoretically, using derived robot dynamics and experimentally that the CPG-based online gait generation method allows continuous and rather smooth transitions between gaits. Lastly, we present an application where the snake robot is guided from an initial to final position while avoiding obstacles by changing CPG parameters.     

双足机器人自适应常值驱动与传感反馈结合的仿生行走控制

为了将双足机器人的混沌步态控制收敛到稳定的周期步态,提出一种控制策略。首先用庞卡莱截面法研究斜坡倾角变化对步态的影响,结果表明,坡度增大会导致倍周期步态到混沌步态的产生;然后以人类步行的生物力学为仿生依据,根据延迟反馈控制的基本思路,设计了自适应常值驱动与传感反馈相结合的仿生行走控制策略,并依据当前步和前两步初始状态对控制器参数进行逐步调节,最终将混沌步态控制收敛到周期步态。仿真结果表明了所提出算法的有效性。     

Optimal Trajectories for a Quadruped Robot with Trot,Amble and Curvet Gaits for Two Energetic Criteria

In this paper, optimal cyclic reference trajectories aredesigned for three gaits of a quadruped robot, the curvet, theamble, and the trot, taking into account the actuatorscharacteristics. The gaits are composed of stance phases andinstantaneous double supports. The principle of virtual leg isused to obtain simpler dynamic model describing the motion ofthe quadruped. The impact phases are modeled by passive impactequations. For the curvet the step is composed of twodifferent half steps. For the amble and trot gaits twofollowing half steps are symmetrical.The optimization problem is solved with an algebraicoptimization technique. The actuated joint evolution is chosenas a polynomial function of time. The coefficients of thepolynomial functions are optimization parameters. Thequadruped studied has non-actuated ankles. The kineticmomentum theorem permits to define the evolution of this non-actuated variable in function of the actuated variables. Twoenergetic criteria are defined: a torque cost and an energetic cost. The first is represented by the integral of the torquenorm and the second by the absolute value integral of theexternal forces work. The two criteria are calculated for adisplacement of one meter. During the optimization process,the constraints on the ground reactions, on the validity ofimpact, on the torques, on the joints velocities and on themotion velocity of the robot prototype are taken into account.Simulation results are presented for the three gaits. Allmotions are realistic. Curvet is the less efficient gait withrespect to the criteria studied. For slow motion, trot is themore efficient gait. But amble permits the fastest motion withthe same actuators.     

Dynamically balanced optimal gaits of a ditch-crossing biped robot

This paper deals with the generation of dynamically balanced gaits of a ditch-crossing biped robot having seven degrees of freedom (DOFs). Three different approaches, namely analytical, neural network (NN)-based and fuzzy logic (FL)-based, have been developed to solve the said problem. The former deals with the analytical modeling of the ditch-crossing gait of a biped robot, whereas the latter two approaches aim to maximize the dynamic balance margin of the robot and minimize the power consumption during locomotion, after satisfying a constraint stating that the changes of joint torques should lie within a pre-specified value to ensure its smooth walking. It is to be noted that the power consumption and dynamic balance of the robot are also dependent on the position of the masses on various links and the trajectory followed by the hip joint. A genetic algorithm (GA) is used to provide training off-line, to the NN-based and FL-based gait planners developed. Once optimized, the planners will be able to generate the optimal gaits on-line. Both the NN-based and FL-based gait planners are able to generate more balanced gaits and that, too, at the cost of lower power consumption compared to those yielded by the analytical approach. The NN-based and FL-based approaches are found to be more adaptive compared to the other approach in generating the gaits of the biped robot.     

Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot

Minimization of energy consumption plays a key role in the locomotion of a multi-legged robot used for various purposes. Turning gaits are the most general and important factors for omni-directional walking of a six-legged robot. This paper presents an analysis on energy consumption of a six-legged robot during its turning motion over a flat terrain. An energy consumption model is developed for statically stable wave gaits in order to minimize dissipating energy for optimal feet forces distributions. The effects of gait parameters, namely angular velocity, angular stroke and duty factors are studied on energy consumption, as the six-legged robot walks along a circular path of constant radius with wave gait. The variations of average power consumption and energy consumption per unit weight per unit traveled length with the angular velocity and angular stroke are compared for the turning gaits of a robot with four different duty factors. Computer simulations show that wave gait with a low duty factor is more energy-efficient compared to that with a high duty factor at the highest possible angular velocity. A stability analysis based on normalized energy stability margin is performed for turning motion of the robot with four duty factors for different angular strokes.     

Two walking gaits for a planar bipedal robot equipped with a four-bar mechanism for the knee joint

The design of a knee joint is a key issue in robotics and biomechanics to improve the compatibility between prosthesis and human movements, and to improve the bipedal robot performances. We propose a novel design for the knee joint of a planar bipedal robot, based on a four-bar linkage. The dynamic model of the planar bipedal robot is calculated. Two kinds of cyclic walking gaits are considered. The first gait is composed of successive single support phases with stance flat-foot on the ground separated by impacts. The second gait is a succession of finite time double support phases, single support phases, and impacts. During the double support phase, both feet rotate. This phase is ended by an impact of the toe of the forward foot, while the rear foot is taking off. The single support phase is ended by an impact of the swing foot heel, the other foot keeping contact with the ground through its toe. For both gaits, the reference trajectories of the rotational joints are prescribed by cubic spline functions in time. A parametric optimization problem is presented for the determination of the parameters corresponding to the optimal cyclic walking gaits. The main contribution of this paper is the design of a dynamical stable walking gait with double support phases with feet rotation, impacts, and single support phases for this bipedal robot.     

Self-organized adaptive legged locomotion in a compliant quadruped robot

In this contribution we present experiments of an adaptive locomotion controller on a compliant quadruped robot. The adaptive controller consists of adaptive frequency oscillators in different configurations and produces dynamic gaits such as bounding and jumping. We show two main results: (1) The adaptive controller is able to track the resonant frequency of the robot which is a function of different body parameters (2) controllers based on dynamical systems as we present are able to “recognize” mechanically intrinsic modes of locomotion, adapt to them and enforce them. More specifically the main results are supported by several experiments, showing first that the adaptive controller is constantly tracking body properties and readjusting to them. Second, that important gait parameters are dependent on the geometry and movement of the robot and the controller can account for that. Third, that local control is sufficient and the adaptive controller can adapt to the different mechanical modes. And finally, that key properties of the gaits are not only depending on properties of the body but also the actual mode of movement that the body is operating in. We show that even if we specify the gait pattern on the level of the CPG the chosen gait pattern does not necessarily correspond to the CPG’s pattern. Furthermore, we present the analytical treatment of adaptive frequency oscillators in closed feedback loops, and compare the results to the data from the robot experiments.

Near-optimal gait generations of a two-legged robot on rough terrains using soft computing

A two-legged robot will have to generate its near-optimal gaits after ensuring maximum dynamic balance margin and minimum power consumption, while moving on the rough terrains containing some staircases and sloping surfaces. Moreover, the changes of joint torques should lie below a pre-specified small value to ensure its smooth walking. The balance of the robot and its power consumption are also dependent on hip trajectory and position of the masses on various limbs. Both neural network- and fuzzy logic-based gait planners have been developed for the same, the training of which are provided using a genetic algorithm off-line. Once optimized, the planners are found to generate optimal gaits of the two-legged robot successfully for the test cases.     

Gait transition for a quadrupedal robot by replacing the gait matrix of a central pattern generator model

The pattern-generator-based approach for legged robot control is inspired by biological neural mechanisms of locomotion, in which a special challenge is gait transition. In this paper we build a holosymmetric central pattern generator model and propose parameter-setting principles for a gait matrix capable of producing typical quadrupedal gaits, and based on them present an approach of directly replacing the gait matrix for gait transition, with a focus on three problems emerging during transition: breakpoint, phase-lock and oscillation-stop. Breakpoints are smoothed by remaining the current outputs during transition, similar to a zero-order holder. Breaking the phase-lock is accomplished by adding a perturbation to the state matrix at the transiting point. An oscillation-stop of less than one period can be ignored. With such treatments, it is proved that gait transitions between any two gaits on a quadrupedal robot can be achieved at arbitrary phase locations in a walk cycle, theoretically and experimentally in part.     

Kinematic Constraints on Fault-Tolerant Gaits for a Locked Joint Failure

Fault-tolerant gaits in legged locomotion are defined as gaits with which legged robots can continue their walking after a failure event has occurred to a leg of the robot. For planning an efficient fault-tolerant gait, kinematic constraints and remaining mobility of the failed leg should be closely examined with each other. This paper addresses the problem of kinematic constraints on fault-tolerant gaits. The considered failure is a locked joint failure which prevents a joint of a leg from moving and makes it locked in a known place. It is shown that for the existence of the conventional fault-tolerant gait for forward walking on even terrain, the configuration of the failed leg must be within a range of kinematic constraints. Then, for coping with failure situations where the existence condition is not satisfied, the conventional fault-tolerant gait is adopted by including the adjustment of the foot trajectory of the failed leg. The foot trajectory adjustment procedure is analytically derived to show that it can help the fault-tolerant gait avoid dead-lock resulting from the kinematic constraint. To demonstrate its effectiveness, the proposed method is applied to the fault-tolerant gait generation for a quadruped robot walking with the wave-crab gait before a locked joint failure.     

Omnidirectional static walking of a quadruped robot

In this paper, we propose a successive gait-transition method for a quadruped robot to realize omnidirectional static walking. The gait transition is successively performed among the crawl gaits and the rotation gaits, while the feet hold in common positions before and after gait transition. The gait-transition time is reduced by carefully designing the foot positions of the crawl gait and the rotation gait, while limiting the feet in rectangular reachable motion ranges. Computer simulations and experiments were executed to show the validity and the limitation of the proposed gait-transition method.     

Implementation of omnidirectional crawl for a quadruped robot

As a reptile animal crawls in a cluttered environment, so a quadruped robot should be able to crawl on an irregular ground profile with its static stability by adopting the straightgoing and standstill-turning free gaits. The generalized and explicit formulations for the automatic generation of straight-going gaits and various standstill-turning gaits are presented in this paper. The maximized stride for the straight-going gait and the maximum turning angle for the turning gait of a quadruped robot named TITAN-VIII in a gait cycle are discussed by considering the robot's mechanism constraints and the irregularities of the ground profile. The control algorithm, including control of the joint positions of the robot, is described to implement the desired walking path of the quadruped robot. The effectiveness of the proposed method is demonstrated through experimental result.     

仿蟹机器人步态分析与仿真

在仿蟹机器人的行走控制中,步态的选择对机器人的稳定快速行走具有至关重要的作用。本文对仿蟹八足机器人的基本步态进行了分类,并进一步对八足波形步态进行分析,得出八足步行机器人在采用双四足步态的行走方式时,既可以满足速度的要求,又可以保证机器人的稳定性。通过计算机软件ADAMS对所选步态进行全局仿真,结果验证了步态规划的合理性,同时得到了机器人相关物理量的变化曲线,为进一步选择电机,分析机器人系统的动态特性提供了依据。     

六边形对称分布六腿机器人的典型步态及其运动性能分析

为了便于在不同地理条件下合理地选择较优的步态,实现稳定高效的智能行走,本文针对一种六边形 对称分布的六腿机器人研究其不同步态的优劣．主要从行走能力、稳定性和能耗3 个角度对六边形对称结构的六腿 机器人在同样占空比下的3 种静态稳定周期步态进行了比较研究,此外还简要分析了其越障能力和穿越窄道的能 力．研究分析结果表明3 种步态（横向昆虫式摆动步态、哺乳动物式踢腿步态和混合步态）在不同条件下各有优劣： 横向昆虫式摆动步态在能耗和越障能力方面较其他两种步态有优势;而混合步态在稳定性上最具优势,其它能力处 于中间;哺乳动物式踢腿步态则可穿越窄道,步长上较昆虫摆动步态略好．本文的研究工作为六边形对称结构的六 腿机器人在未知复杂地貌环境下的智能行走提供了重要参考．     

Energy-preserving control of a passive one-legged running robot

Fast and energy-efficient control is an increasingly important and attractive area of research in legged locomotion. In this paper, we present a new simple controller for a planar one-legged passive running robot having a springy leg and a compliant hip joint. The most distinctive advantage of the controller over previously proposed ones is it does not require any pre-planned trajectories nor target dynamics. Instead, it utilizes exact non-linear dynamics. Our results are summarized as follows. First, we propose an energy-preserving control strategy for energy-efficient and autonomous gait generation. This strategy is successfully implemented as a new touchdown controller at the flight phase. Simulation results show that the robot can hop from a wide set of initial conditions. Moreover, the running gaits generated are found to be quasi-periodic orbits, which can be seen in Hamiltonian systems. Since the controlled running gaits exist for every admissible energy level, they have some robustness against disturbances. Next, it is shown that an adaptive control of the touchdown angle, which is similar to a delayed feedback controller for a chaotic system, can asymptotically stabilize these quasi-periodic gaits to the periodic ones of the desired period, with some limitations. In particular, for one-periodic gait, by using some additional adaptive controllers, the robot eventually hops without any control inputs. Since our energy-preserving strategy is clear and implementation of the controller is straightforward, we believe it can be easily applied to a wide class of legged mechanisms.     

Development of wheel-less snake robot with two distinct gaits and gait transition capability

Snake robots are mostly designed based on single mode locomotion. However, single mode gait most likely could not work effectively when the robot is subject to an unstructured working environment with different measures of terrain complexity. As a solution, mixed mode locomotion is proposed in this paper by synchronizing two types of gaits known as serpentine and wriggler gaits used for non-constricted and narrow space environments, respectively, but for straight line locomotion only. A gait transition algorithm is developed to efficiently change the gait from one to another. This study includes the investigation on kinematics analysis followed by dynamics analysis while considering related structural constraints for both gaits. The approach utilizes the speed of the serpentine gait for open area locomotion and exploits the narrow space access capability of the wriggler gait. Hence, it can increase motion flexibility in view of the fact that the robot is able to change its mode of locomotion according to the working environment.     

Fault-tolerant locomotion of the hexapod robot

In this paper, we propose a scheme for fault detection and tolerance of the hexapod robot locomotion on even terrain. The fault stability margin is defined to represent potential stability which a gait can have in case a sudden fault event occurs to one leg. Based on this, the fault-tolerant quadruped periodic gaits of the hexapod walking over perfectly even terrain are derived. It is demonstrated that the derived quadruped gait is the optimal one the hexapod can have maintaining fault stability margin nonnegative and a geometric condition should be satisfied for the optimal locomotion. By this scheme, when one leg is in failure, the hexapod robot has the modified tripod gait to continue the optimal locomotion.     

Planar legged walking of a passive-spine hexapod robot

This paper proposes a new legged walking method for a novel passive-spine hexapod robot. This robot consists of several body segments connected by passive body joints. Each of the body segments carries two 1-DoF (degree of freedom) actuated legs. The robot is capable of achieving planar legged walking by rapidly abducting and adducting its legs. To model the mobility of a robot based on this simple design, the candidate configurations from all possible configurations are first selected in a mobility analysis of the robot based on the screw theory. All the feasible sequences of these candidate configurations are then searched to form planar locomotion gaits. Next, locomotive performance of the gaits is analyzed. Finally, the proposed locomotion design and gait planning methods are verified through simulations and experiments.