Analysis of the non-reciprocating legged gait for a hexapod robot based on the ePaddle-EGM
© The Author(s) 2016
Received: 28 February 2016
Accepted: 9 March 2016
Published: 28 June 2016
A novel eccentric paddle mechanism based on the epicyclic gear mechanism (ePaddle-EGM) has been proposed to enhance the mobility of amphibious robot for multi-terrain tasks with diverse locomotion gaits. This paper presents a brief description for this mechanism. Based on the feature of ePaddle-EGM, a unique non-reciprocating legged gait planning method is proposed. This method could minimize the negative effect of backlash between gear mesh in the epicyclic gear mechanism. Furthermore, the stable tripod gait for the ePaddle-EGM-based hexapod robot is designed. One of the most important characteristics of this tripod gait is that it is capable of realizing discontinuous locomotion of the body through continuous and unidirectional rotation of joints. In this way, the velocity shock is eliminated and the locomotion accuracy is guaranteed. A series of simulations were conducted to validate the advantages of the robot’s movement.
Due to the strong environmental adaptability in harsh environments such as land, water and beach, amphibious robots can perform various tasks for human, such as environmental monitoring, resource exploration, disaster rescue and underwater mine clearing. This makes amphibious robots have a wide application prospect. Researchers have paid more and more attentions to the novel structure design, control and navigation of the amphibious robot, to improve its mobility in multi-environments. Various types of amphibious robots have been built. One of the most remarkable types is the biomimetic amphibious robot, which is inspired from the morphological feature of natural creatures. By learning and imitating the biologic characteristics and function of their biologic counterparts, this type of amphibious robots then reproduces these characteristics, such as Salamander I  and II  by Crespi, Pleurobot by Karakasiliotis , ACM-R5 by Yamada , Ariel by Yamauchi  and MLMR II by Deng . Besides, researchers have also developed several novel robotic mechanisms to achieve amphibious mobility, by integrating several basic motion units into one locomotion mechanism. For instance, the wheel–leg–tail integration robot DAGSI Whegs developed by Boxerbaum , paddle–wheel integration autonomous amphibious vehicle developed by Frejek  and leg–paddle integration robot AQUA .
Instead of focusing on the design of propulsive mechanism for simple environment, we have proposed a novel hybrid-mechanism-based amphibious propulsive mechanism in our previous works [10, 11], and it is called the ePaddle-EGM. It is made up mainly of an eccentric paddle and an epicyclic gear train. The ePaddle-EGM is an innovative mechanism which combines wheeled, legged and paddling gaits to perform multi-terrain locomotion for amphibious tasks [12, 13]. High motion performance on multiple terrains can be simply achieved by actively adjusting the position of paddle shaft in the ePaddle mechanism.
However, some problems about the ePaddle-EGM were exposed as well. For example, the backlash between gear meshes may compromise the accuracy of locomotion in legged walking or aquatic paddling modes. Therefore, in order to promote motion accuracy with the natural presence of backlash, we proposed a novel kinematic method based on the idea of generating reciprocating trajectory of the paddle using unidirectional and continuous rotations of the actuators.
In this paper, we briefly introduce the non-reciprocating kinematic method which can overcome the negative influence of backlash. The rest of this paper is organized as follows. The introduction of the ePaddle-EGM module, the non-reciprocating kinematic method and the gait planning method of the ePaddle-based hexapod robot are presented in section ‘Methods.’ The results of simulations for ePaddle-based hexapod robot are listed in section ‘Results and discussion.’ Finally, section ‘Conclusions’ concludes this paper.
The eccentric paddle mechanism
Non-reciprocating kinematic method
The application of epicyclic gear mechanism has brought plenty of advantages for our design, such as the high reliability and high efficiency of the gear train. But at the meantime, the backlash between gear mesh may accumulate during locomotion and then influence the accuracy of the locomotion seriously. On the other hand, generally, the active joints of multi-legged robot have to change their direction of motion frequently during the successive locomotion of robot. The change in the direction of motion may bring in sudden change in joint velocity. So based on these consideration, we have proposed the non-reciprocating kinematic method which will be presented below.
Some of the technical terms needed to describe the gait should be defined before we can proceed further .
A stride is a complete cycle of leg movements, for example, from the setting down of a particular foot to the next setting down of the same foot.
A gait cycle T is the duration of a stride. For legged robot, the gait cycle consists of the stance phase (STP) and the swing phase (SWP). The duty factor ξ is the ratio of duration of STP to a whole gait cycle; in other words, ξ of a foot is the fraction of the duration of the stride for which it is on the ground. In nearly all the gaits used by animals, the left and right feet of a pair have approximately equal duty factors.
λ FSP/λ SSP means the distance of end of each leg traveled in the horizontal direction relative to the hip joint in the first/second stance phase, and λ is the sum of λ FSP and λ SSP; detailed information could be found in article [15, 16].
Features of proposed method
For purpose of improving the motion accuracy and efficiency, we proposed the non-reciprocating kinematic method. Since the detailed information about this kinematic method is not the focus of this paper, so it will not be described here.
The most notable feature of this method is that during the whole locomotion cycle, all the active joints in the mechanism are rotating unidirectionally and continuously. The unidirectivity of active joints can diminish the negative effect of backlash between gear mesh. Because of the continuity, the velocity shock caused by sudden change in joint velocity is also eliminated. Furthermore, since the λ FST and λ SSP could be arbitrary value, when the duration of first/second stance phase is constant, we can change velocity of ePaddle-EGM immediately. At present, since the rotary of each active joint is unidirectional and continuous, it means the ePaddle-EGM is capable of altering the locomotion pattern smoothly and instantaneously.
The ePaddle-based hexapod robot
Generally, there are two types of gaits adopted in mobile robot—periodic gait and non-periodic gait which is called free gait as well . The former could increase the adaptability of the mobile robot because it can let robot move on the uneven terrain. However, the free gait is difficult to be realized in the real multi-legged mobile robots and is only on the stage of theoretical research. Periodic gait such as tripod gait can be easily controlled and has an optimal stability margin . So in this section we will be concentrated on realizing the non-reciprocating tripod gait of the ePaddle-based hexapod robot.
Uniform rectilinear motion
Variable rectilinear motion
Normally, when mobile robot receives the command of switching its locomotion pattern (e.g., changing the forward velocity), it is difficult for the trunk to reach the setting velocity immediately, because it requires all the actuators to accelerate or decelerate for a certain time. As a result, since the adjustment of rotational velocity of each actuator may take some time, so the real-time performance of robot may be compromised. On the other hand, if altering the rotational velocity of actuators within a wide range in a short time, it may damage the actuate components or transmission components. Therefore, for mobile robots, in consideration of safety of system, the adjustment time between two different locomotion patterns is necessary and inevitable.
Nevertheless, it is not true for ePaddle-based multi-legged robot. In the previous section, we have mentioned that the ePaddle-EGM is capable of altering the locomotion pattern smoothly and instantaneously. Since the λ FST and λ SSP could be arbitrary value (of course within its work space), when the duration of first/second stance phase is constant, the ePaddle-EGM can alter its forward velocity instantly, without sudden change in rotational velocity and reciprocating rotation of each driving joint. In other word, the switch between different locomotion patterns can be realized immediately. This non-reciprocating strategy can also be applied in the ePaddle-based hexapod robot to realize the fast transition of locomotion pattern. We will validate this in next section.
Turning gait is very important for the mobility of robot. Since each ePaddle-EGM module only has three DOFs in the plane of shell, the leg (supporting paddle) actuation is limited to motion in the sagittal plane. However, via differential motion between left and right modules, it is possible for ePaddle-based hexapod robot to realize turning motion. Due to unidirectional rotation of all the actuators during the legged gait, each ePaddle-EGM module cannot move in the opposite direction. Hence, the robot cannot turn in place. But through configuring different strides for legs of both sides, the robot can turn during running. In order to verify the ability to turn, the robot is simulated to turn with varying radii in this paper.
Results and discussion
In this section, we conducted simulations to verify our proposed non-reciprocating legged walking gait for an ePaddle-based robot. The robot contains a trunk body and six ePaddle-EGM modules. For the simplicity, the configuration of the body is a rectangular parallelepiped. The simulations were conducted in multi-body dynamics simulator called Recurdyn (FunctionBay, Inc.). In these simulations, test trials are performed on an even terrain. The mass and inertia properties of the ePaddle component are extracted from CAD software. The coefficient of friction between the terrain and tips of paddle is taken to be equal to 0.8. The simulations have been performed with two cases: (1) variable rectilinear motion, which means walking along a straight-line path with different velocities, and (2) turning motion with varied radii. Since the uniform rectilinear motion is a relatively simple behavior, so the simulation of it has been omitted here.
In this paper, a novel kinematic method for the ePaddle-EGM has been proposed. The distinguishing feature of this kinematic method is that it is capable of realizing discontinuous locomotion of the body through continuous and unidirectional rotation of actuators. In this way the influence of backlash in the epicyclic gear mechanism could be eliminated and accuracy of locomotion can be guaranteed. Based on this non-reciprocating kinematic method, we proposed the tripod gait planning method for the packsaddle-based hexapod robot to realize its stable motions, including the uniform rectilinear motion, the variable rectilinear motion and turning motion. The studies of simulations have been conducted to verify the performance of the tripod walking gait; namely, the hexapod robot can switch between different locomotion patterns instantly.
JZ and HP have jointly carried out the development of ‘The eccentric paddle mechanism’ section, ‘Non-reciprocating kinematic method’ section and ‘ePaddle-based hexapod robot’ section. JZ revised and completed all the figures. Finally, YS and SM have jointly written ‘Introduction’ section. All authors read and approved the final manuscript.
This work was financially supported by the National Natural Science Foundation of China under Grant Number of 61305127.
The authors declare that they have no competing interests.
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