Abstract—This paper presents simulation and analysis on dynamics of a hybrid mobile robot. The robot is designed to take advantage of both rolling and jumping locomotion ways on the ground. The most outstanding feature of the robot is the minimum use of actuator. The robot is designed to be able to execute both jumping and rolling skillfully by using only one DC motor. Mechanism design and control logic are validated by computer simulation.

I. INTRODUCTION One type of locomotion method for a ground mobile robot

may not be suitable for many different kinds of working environment. Therefore a hybrid mobile robot that is able to employ multiple types of locomotion skills can be really a viable solution. A variety of works to incorporate jumping and rolling in one mobile robot have been reported. Jollbot [1] is one of the examples that is capable for both jumping and rolling. Although the robot can execute both locomotion types, overall performance is not considered quite remarkable. The spherical robot with 300 mm diameter can jump up to 0.6 times its height but it has a weak ability in the rolling.

Scout [2, 3] is another example in the category. The robot is quite skillful in both jumping and rolling. This robot with 40 mm diameter can jump up to 100 mm and run at 310 mm/sec. Besides, this robot can easily steer to change the moving direction. However complexity in the structure is a disadvantage of the robot, which is due to many actuators.

Sugiyama and his coworkers introduced a crawling-jumping robot [4] that is actuated by SMA (shape memory alloy). The robot uses SMA as an actuator and employs deformation principle for rolling. This work suggests a new way of using unconventional actuators for hybrid mobile robots.

Though incorporating multiple locomotion ways in one robot can increase its maneuverability, energy efficiency may be reduced. It is because the number of actuators on a robot is larger than or equal to the number of locomotion gaits. Increasing the number of actuators leads to increase of weight, size, and complexity. This paper presents development of a robot that can locomote by means of

Manuscript received September 15, 2013. This work was supported by

Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(MEST) (2011-00260).

Thanhtam Ho, Hwiyong Choi, and Sangyoon Lee are with Department of Mechanical Design and Production Engineering, Konkuk University, Seoul, 143-701 South Korea (phone: 822-450-3731; e-mail: slee@konkuk.ac.kr). Thanhtam Ho is presently with Neuromeka, Gyeonggi-do, South Korea.

jumping and rolling using only one actuator. In particular simulation and analysis on dynamics of a hybrid mobile robot is reported.

II. ROBOT DESIGN Our proposed robot is designed to execute rolling by

changing the center of gravity (COG) [5]. There are multiple ways to change the COG position: rotating a mass around a centerline or sliding a mass along an axis. These rolling methods can be realized with only one actuator like a rotational motor. In the sliding mass method, the mass is moved only in a short range along a linear direction. This motion can also be utilized to extend a spring for jumping.

The robot has a cylindrical cage and the cage will act as a wheel for rolling and as a balance cage for recovering the stable posture after jumping. A contact area between the robot and the ground at each section is only one point. This makes the robot become sensitive to the change of COG. It means that the robot is easy to roll. The robot contains a slider part which can slide along a rack to change the COG position.

A main component of the slider is a DC motor with a pinion that is attached to the motor shaft. A gear is linked to a rack element fixed on the body case. The rack and pinion mechanism converts rotation of the motor to translation of the slider along the body.

In jumping mode, the slider is able to move between the highest position and the lowest position. The slider has a small element called the limited latch. The latch is designed especially for the jumping locomotion. There is also another element, the hook, which is used for jumping. The hook is fixed on the leg and frame. In rolling mode, the latch and the hook are kept separated and they do not have any function.

In jumping, the latch on the slider and the hook of the leg take an important role. They enable the energy generated by the DC motor to be stored in the spring. Also, these two devices act as an energy releasing mechanism that frees the energy for jumping.

Overall robot design is presented in Fig. 1. The robot is made of four basic parts: the frame with leg (1), the main spring (2), the body base (3), and the slider (4). The frame contains a cylindrical shell welded with a rod which is called the robot leg.

Simulation and Analysis on Dynamics of a Minimally-Actuated Hybrid Mobile Robot

Thanhtam Ho, Hwiyong Choi, and Sangyoon Lee

978-1-4799-2744-9/13/$31.00 ©2013 IEEE

Proceeding of the IEEEInternational Conference on Robotics and Biomimetics (ROBIO)

Shenzhen, China, December 2013

414

Fig. 1. Overall design of the rolling-jumping robot with four major

modules. When the jumping mechanism was designed, jumping

mechanisms of insects have been studied. In general, fundamental principles are based on the energy storage system. Compared to directly activated jumping mechanisms such as the authors’ previous jumping robot [6], jumping mechanisms of insects possess larger advantage in terms of jumping distance and jumping height. The froghopper is one outstanding example [7]. While the froghopper prepares for jumping, energy generated by the insect’s muscle is gradually stored in a resilient part. The energy is quickly released for the insect to jump up to the air [8]. Rapid release of the stored energy is a key element for a successful jumping. Since the proposed robot is actuated by only one actuator which will function as the energy generator, energy needs to be released passively.

In order to start a jumping motion, the slider moves downward to the hook position. Due to the pushing force of the hook, the latch rotates around its revolute joint. When the slider continues to go downward to the lowest position, the latch contacts the hook no longer and it is rotated back to its original position by the torsion spring. It is noted in Fig. 3 that vs indicates the velocity of the slider with respect to the body base and vb is the velocity vector of body with respect the robot leg. From the lowest position the slider moves upward. In this direction, the latch is locked to hook (see Fig. 3(b)) and therefore its absolute velocity becomes zero. Rotation of the DC motor moves the body downward with the velocity vb. Since the main spring is connected to the rod and the body base, motion of the body results in the compression of the spring. This is called the energy storage procedure where the energy generated by the DC motor is stored in the main spring.

Fig. 2. Jumping mechanism of the robot.

III. COMPUTER SIMULATION AND ANALYSIS Rolling of the proposed robot is produced indirectly by the

motion of slider. A mathematical model of rolling will be useful for developing the control method for the robot. Rolling model is developed with an assumption that the robot rolls on the ground without slipping. Since the robot is not able to move laterally, it can be simplified a 2D circular model.

Dynamics model of the rolling robot is displayed in Fig. 3 and the parameters of model are described in Table I. For analysis, Euler’s equation is used to compute the rotational moments while Newton’s second law is utilized for translational components. If C is the temporary rotation center for moment computation and ICM is moment of inertia of whole robot with respect to the frame’s center, one can get equation of motion as in (1) where displacement of slider d is input variable and rotation angle θ is output quantity.

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Fig. 3. Rolling dynamics model.

TABLE I PARAMETERS OF ROLLING DYNAMICS MODEL.

Symbol Description

θ Tilt angle of robot body α Angular acceleration v Longitudinal velocity at circle center a Longitudinal acceleration at circle center

m1 Mass of frame and robot body

m2 Mass of slider fS Static friction force d Displacement of slider

( )2 2 2 2 2 21 112 2

cos

F B S t S

S

m R m H W m r M R m d

m gd

θ

θ

⎛ ⎞+ + + + +⎜ ⎟⎝ ⎠=

(1)

The dynamics model is first used for analyzing responses.

A step function is selected as the input variable and slider displacement, rolling velocity, and rolling angle are recorded. By changing the magnitude of the step input, output quantities are observed and displayed in Fig. 4.

Fig. 4 displays response of the system in three different cases. In all cases system parameters are kept same except the magnitude if step input. It is observed the responses that when the step height increases not only magnitude of rolling speed increase but its frequency also increases.

Fig. 4(a) shows response to 10 mm step input, and in this case rolling speed varies with peak of 2.22 rad/sec and frequency of 0.28 Hz. In case of 20 mm step input (see Fig. 4(b)) rolling speed increases to 3 rad/sec peak and vibrates at 0.4 Hz. In the last case shown in Fig. 4(c) where 30 mm step height is used the frequency of rolling speed reach 0.5Hz and 3.8 rad/sec peak. This result suggests that by changing motion range of slider one can control rolling speed of the robot.

The second test with the rolling dynamics model is done with control algorithms. The control algorithm mimics ideas of rolling principle. It means that the robot must keep slider in

front of circle center in order to move forward. Here a feedback controller is used to adjust the slider position. The control rule is shown in (2).

cosCu K θ= (2)

In (2), cosθ indicates the relative position of the robot

centerline with respective to a vertical line. It indicates whether the robot is leaning forward or not to move the slider to a proper position. The gain KC represents translation speed of the slider along body axis. The test is performed for three cases where gain KC is 0.005, 0.01 and 0.02 respectively.

The test provides important results to control the rolling motion. First, they clarify the principle of rolling control. Forward rolling is obtained by keeping the slider position in front of the frame center. The second result is about effect of slider speed to robot rolling speed. By increasing the feedback gain KC, or slider speed, rolling speed also increases dramatically.

(a)

(b)

(c)

Fig. 4. Step responses of rolling system: (a) response to 10 mm step input, (b) response to 20 mm step input, (c) response to 30 mm step input.

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The energy cost of transport is a commonevaluate energy efficiency of locomotiontransport is measured by the essential energymass in a unit distance. If EKE is required perform a locomotion gait and M is mass moving distance, cost of transport of the ga(3). Cost of transport varies for different localso changes with weight, size of robottransport means less energy for traveling and hence higher efficiency.

KEEC

Md=

If data of the proposed rolling-jumping r

can roughly compute cost of transport of rolSince R = 0.09 m, v = 0.6 m/sec, and α = 20transport of rolling and jumping are respectively. Therefore cost of transport of larger than that of rolling. It is because a jumto spend energy to leap whole body off grouone is supported by ground.

In order to evaluate energy efficiency rolling-jumping robot, its cost of transport compared to that of Scout and Jollbot 3b robots are selected because they employ a sias ours: rolling and jumping. Besides, all useactuator. Major differences of these robots aactuators, system complexity, body size, an3b is the largest one and utilizes two RC sRolling-jumping robot is the lightest one wmotor.

Among the three robots, our rolling-julowest cost of transport in both rolling anThough Jollbot 3b is the largest robot, it most expensively. It may be because rollinindirectly controlled by rotation of a balanwheels of Scout are directly connected to mthe rolling-jumping robot is also indirectly slider but it has only one actuator. Minimactuator reduces weight, complexity and elost. Therefore it still shows the best energlowest jumping cost of transport is also explaway, as shown in Fig. 4. Using single acadvantage to increase energy efficiency rolling-jumping robot.

n quantity used to . Energy cost of

y to move a unit of kinetic energy to of robot and d is

ait is defined as in comotion gaits. It t. Lower cost of a given distance,

(3)

robot is used, one ling and jumping.

0 deg, the costs of 0.64 and 7.63, jumping is much

mping machine has und while a rolling

of the presented is calculated and robot. These two imilar locomotion e electric motor as are the number of nd weight. Jollbot servo motors and

with only one DC

umping robot has nd jumping gaits.

performs rolling ng of Jollbot 3b is nce device while

motors. Rolling of controlled by the

mizing the use of especially energy

gy efficiency. The ained by the same

ctuator is the key of the presented

Fig. 4. Cost of transport in jumping of thJollbot, Scout, and our rolling-jumping robot

Working of the robot mechanism

been verified through computer jumping and rolling motions in planin the lateral direction is neglected 2D simulation software Working selected for the dynamics simulationimplemented using Matlab softwarscheme the communication between performed by the dynamics data exc

The input data for the controlleWM2D to Matlab software and the oin Matlab is sent to the DC motordesign model presented is directly imbuild the dynamics simulation mode

Motion of the DC motor in the pcontrols the rolling and the jumpimodel is considered for the autonomcontroller receives the task from tdirectly with the environment. It alcommands to the low level concontroller adjusts the rotation of throbot to perform basic motions inbackward rolling, stopping, and jum

The low level controller moves thorder to perform the specific motiocontrol parameters for the low level cand the motion speed of the robot.must be kept in front of the cylindefor the robot to roll forward. In simulwhich combines several rules is utili5 presents flowchart of control logic

0

5000

10000

15000

20000

25000

Jollbot Scout

Cost of transport

hree hybrid locomotion robots: .

and the control logic has simulation. Since only

ne are introduced, motion for the simulation work. Model 2D (WM2D) is

n purpose. Control logic is re. In this co-simulation two software packages is

change protocol (DDE). ers are transferred from output from the controller r model in WM2D. The mported to the WM2D to el. proposed robot indirectly ing. A two-level control

mous tasks. The high level the user or is interfaced so decides and gives the ntroller. The low level he motor in order for the ncluding forward rolling, mping. he slider along the rack in ons given by users. The controller are the position For example, the slider

er frame’s center in order lation, a simple controller ized for this purpose. Fig. c for forward motion.

t Our robot

t (Jumping)

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Fig. 5. Forward motion control logic. The first simulation set was done to evaluate the jumping

locomotion. The spring stiffness is kept at 0.36 N/mm while the tilt angle of the robot is changed from 10 to 25 degree. Two low level control algorithms for jumping and stopping were executed. The average time to execute a jump is about 1 second however the stabilizing time after each jump is about 4 seconds. For the range of tilt angle, the jumping height was in the range of 200~230 mm and the jumping distance was in the range of 180~218 mm.

The second simulation set was designed to verify the rolling motion. Here all basic motions employed by the low level controller were executed in sequence. The rolling speed, the response time of the low level controller were examined from this simulation. Besides, the effect of the slider’s speed on the rolling velocity was also evaluated.

In this simulation, the compound motion is supervised by the high level controller. From 1 sec to 5 sec the robot was commanded to roll forward. After that, the rolling changed direction and moved backward to 9 sec. At last, the robot rolled forward again with slower velocity and stopped at 13 sec. The robot performed rolling completely with given commands. Although it is hard to keep the instantaneous velocity constant, its average value is somewhat satisfactory

to the requirements. Especially, during the interval from 10 sec to 13 sec where the sliding speed of the slider was reduced, the forward rolling velocity was also decreased compared to that in the forward rolling (from 1 sec to 5 sec). This is considered as an important result which is used to control the rolling speed of the actual robot.

IV. CONCLUSION Simulation and analysis of a novel jumping and rolling

robot are presented. The most outstanding feature is the minimum use of actuator. By using only one DC motor the robot is still able to perform both jumping and rolling agilely. A tilt angle measurement method for rolling is also developed. The method is validated through simulation and applied for control algorithm. Achievements from the robot can be summarized as: first, using hybrid locomotion of rolling and jumping, the robot may adapt itself to various types of terrain. On the flat surface the rolling locomotion is utilized while the jumping is useful for overcoming obstacles. This can enhance both maneuverability and efficiency of the robot. Second, minimizing the number of actuator to one reduces size, weight, complexity and power consumption of the robot. The energy efficiency is improved as a result.

Fabrication of a robot prototype and experiments are now in the ongoing phase. Parameters of the prototype were selected from the design and simulation results. Jumping experiments are going to be executed with two purposes: first to validate the working principle of the hook-latch mechanism and second to evaluate the jumping performance of the robot prototype. In addition rolling experiments will be also executed.

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