Design and Operation of a
2-DOF Leg-Wheel Hybrid Robot
Erika Ottaviano and Pierluigi Rea
Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Cassino, Italy Email: ottaviano/[email protected]
Received 23 October 2012, Revised on 16 February 2013.
Abstract
In this paper the design and operation are presented for a 2-DOF (Degree-Of-Freedom) leg-wheel hybrid mobile robot. A prototype of a low-cost and easy-in-use system, which is capable of a straight walking and steering with two actuators only, has been designed and built.
Simulation and experimental tests have been carried out to verify the engineering feasibility and operation of the proposed solution. The designed robot can be used for applications such as surveillance or inspection of disaster sites.
Keywords: Walking Robots, Hybrid Mobile Robots, Kinematics, Simulation, Experimental tests.
1. Introduction
Over the last decades, walking machines have posed an interesting field of research, due to their great potential features1. Mobile robots have a wide range of applications such as: inspection, service2, defense, manufacturing, cleaning, remote exploration3, rescue4 and entertainment. In general they can be grouped into two main types, legged and wheeled robots, with important differences in features, as regarding to mechanical design and control systems.
In the near future, robots will interact with human beings in the same environment, which means that the robot design should be suitable for moving in an environment whit stairs, obstacles, and so on, where humans live5. However it is difficult to generate human- like walking motion automatically. Humans can walk not only on flat surface but also on rough terrain, such as steps, obstacles, or slopes. One of the most important advantages of legged robots is the ability to move over rough terrain, even if with a reduced speed. While legged locomotion is more adaptable in a wide range of
ground, wheeled locomotion is faster, but only on smooth surfaces.
The most common walking machines are wheeled and tracked systems, but large interest is also focused on legged machines. A leg tip should generate an approximately straight-line trajectory of a foot point with respect to the body, as obtained in the solutions proposed by [6-8].
A new class of mobile robots can be defined as hybrid systems, for which the advantages of both locomotion types are involved. They have been also developed as combination of wheeled and legged solutions with the aim to exploit the advantages of both types of mobile systems7,8. In [9] a solution is proposed as a leg-wheel hybrid stair climbing wheelchair, which consists of eight independent prismatic-joint legs and eight wheels.
Another prototype is the CALMOS Wheelchair10 that has been developed to improve the mobility of a wheelchair with a four-link mechanism obtaining a staircase- climbing wheelchair. An interesting example for vertical obstacle performance is Tri-Star IV 11, which is a mobile robot designed to explore the moon surface in the near future. Tri-Star IV is composed by two active arms and three active wheels and it can climb vertical obstacles through the two active arms. The prototype in [8] is a hybrid robot with two legs and two passive wheels and hydraulic actuation. A prototype was proposed in [12] in which passive wheels can roll like a skater or walk like a legged robot. The prototype in [13] is a rover with four driving wheels located at the end of the legs.
In this paper a new prototype of leg-wheel hybrid robot is proposed with low-cost easy-operation features. The leg structure has 1 DOF (degree of freedom), indeed it is possible to perform straight walking with one actuator. The steering system is a 1 DOF system for turning ability. Therefore, the proposed prototype has 2 DOFs. Control schemes for the robot were proposed in [14].
E. OTTAVIANO and P.REA 2
sinα B
2 D22
21 3
K 2 4K K In this paper a kinematic analysis of the leg structure
and results are reported of a numerical simulation with design and operation considerations. Then, the design of the 2 DOF prototype is presented together with simulations of its operations. Two solutions for the steering system are simulated and compared. Finally a built prototype is shown together with experimental tests, and considerations on its behavior are outlined.
2. A 1-DOF leg for a walking machine
2.1. Design of the leg2.2. A Kinematic model
A kinematic analysis has been developed in order to evaluate and simulate performances and operations of the leg system. A fixed reference system CXY has been considered attached at body in point C, as shown in Fig.1. The position of point B with respect to CXY frame can be evaluated as a function of the input crank angle α and kinematic parameters of the Chebyshev mechanism LEBDC in the form-letters for table footnotes (Table I).
XB a m cos
c f
cos Each of the two equal legs is composed by Chebyshevand Hart mechanisms, as it is shown in Fig.1. The YB m sin
c f
sin (1)Chebyshev mechanism is used to generate an approximately straight-line trajectory. The lengths of the links are chosen in such a way that the shape of the leg end-point trajectory is similar to the shape of a man’s
The position of point A with respect to the fixed frame can be given as
XA XM
z3 z4
cos 3
z6 z8
cos 6ankle. Moreover, the straight part of the trajectory is
relatively accurate, which is important to limit the body YA
YM
z3 z4
sin 3
z6 z8
sin 6 (2) raising during the walk.The Hart mechanism inverts and amplifies the trajectory. The amplification factor, from point B to point A, is of 2. Thus, the body can move horizontally by moving the legs. Several walking robots have a design containing mechanisms, a class of slider-cranks can be also used for the purpose, according to the results proposed in [15, 16]. Table 1 reports design parameters of the leg system in Fig. 1 as chosen through a
The position of point A1 with respect to the fixed frame can be given as
X A1 X A z 9 cos YA1 YA z 9 sin (3)
The transmission angles in Fig. 1 can be evaluated as parametric analysis. The values of transmission angles,
velocity and acceleration of significant points, and design leg parameters (for example CM=z1) have been determined through a parametric study of the kinematic performance of the system.
1 2
,
3 3 2
2 3 6
(4)
The velocity of points B, A and A1 can be evaluated by using time derivatives from Eqs. (1) to (3). Angles θ, 2,
3 and 6 can be evaluated as
2 tan1 sinα
B D
2 tan1 K
2 2 2K1
L 2 4L L
2tan 1
L 2 1 3
3 2
2L
(5)
M 2 4M M
Figure 1. A kinematic scheme for the proposed 1-DOF leg. 2 tan1
M 2 1 3
6 2
2M
1
1
B
A
A 1 X [m]
0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.2
0 0.2 0.4 0.6 0.8
where
a a a
2 m2 c2 d2 Table 1. Design parameters for model of Fig.1.
B cosα - ;
m D cosα
c 2md
K 2 X z 2 X z X2 X2 z2 Y 2
1 B 2 M 2 B M 2 B
Y2 z2 2 X X 2 Y Y
M 3 B M B M
K2 4 YB z2 4 YM z2
K 2 X z 2 X z X 2 X2
3 B 2 M 2 B M
z2 Y 2 Y2 z2 2 X X 2 Y Y
2 B M 3 B M B M
L 2 X z 2 X z X2 X2 z2 Y2
1 M 3 B 3 B M 3 B
Y2 z2 2 X X 2 Y Y
M 2 B M B M
L 2 4 YB z3 4 YM z 3 L 2 X z 2 X z X2
X2 (6)
z2 Y2
3. A 1-DOF Steering System
In this section two solutions have been analyzed for
3 M 3 B 3 B M 3 B
Y2 z2 2 X X 2 Y Y the steering ability of the hybrid robot, namely:
• Mechanical design to let the wheels turning with
M 2 B M B M
M 1 2 X z G 6 2 X z I 6 XG2 X I2 z62 YG2 respect to an axis passing through H point shown in
Y 2 z2 2 X X 2 Y Y M 2 4 YG z6 4 YI z6
M 2 X z 2 X z X2 X 2 z2 Y2
Y2 z2 2 X X 2 Y Y
Velocity and acceleration of point A1 can be conveniently obtained by differentiating Eq. 3 with respect to time. The proposed analysis has been used for numerical simulations. Numerical results have been obtained without considering the leg’s interaction with the ground.
An amplification factor equal to 2 has been chosen to obtain a foot trajectory with suitable step size, as shown in Fig. 2.
Figure 2. Simulated trajectories for leg operation in leg mechanism in Fig.1.
the scheme of Fig. 3. A suitable motor can be used to drive a mechanism for turning wheels.
• Mechanical design to let the legs rotating with respect to an axis passing through point K, as shown in the schematic representation of Fig. 3. In order to develop this solution the robot chassis should be conveniently divided into 2 parts: one containing the legs (and additional motor) and one containing the rest of the robot body. It is worth to note that in the simplified scheme the legs move remaining parallel.
In both cases the turning capability is related to a rotation of a part of the chassis, one containing the legs and the other with wheels. Thus, the prototype of the walking robot will posses 1 DOF for the steering ability and 1 DOF for the straight walking.
An important issue is the robot stability as related to the steering system. In the following analysis a static or quasi-static behavior of the robot is considered. A very important aspect to consider is the rollover stability of the system, which is closely related to the distance from the robot center of gravity to the boundary of the polygon of the support points OPQ, as shown in Fig.4.
If the steering system is designed by turning wheels, it has the drawback that the above-mentioned distance decreases. When the wheel shaf rotates there is a variation of the position of the support points, which may cause that the projection on the ground of the center of gravity will fall out of the polygon of the supporting points. If this happens the vehicle overturns.
For this reason the maximum allowed rotation angle of the wheels can be evaluated by considering a configuration for which the center of gravity reaches the boundary of a triangle formed by the points OPQ. Figure 4 shows a scheme used to evaluate this angle. It shows
I 7 G I G I
I 7 G I G I
3 G 6 I 6 G I 6 G
Y [m]
a (mm)
m (mm)
c (mm)
d (mm)
f (mm)
45 15 60 60 60
p (mm)
h (mm)
z2 (mm)
z3 (mm)
z4 (mm)
168 104 225 150 150
z5 (mm)
z6 (mm)
z7 (mm)
z8 (mm)
z9 (mm)
225 225 150 225 100
the vehicle's chassis with the wheel shaf rotated by the maximum allowed angle so that the center of gravity lies on the boundary of the polygon in grey color formed by the supporting points OPQ.
Figure 4 shows also main design variables that influence the stability of the prototype for a static analysis. The prototype length has been labeled as L, the distance between wheels A, the distance between the legs supports B, the step of the leg is C, M is the distance from H to the center of mass G of the vehicle, α is the angle of rotation of the wheel shaf.
To calculate the maximum angle of rotation of the wheels αmax one must impose that the ratio between the horizontal and vertical components of the vectors OC QG is the same, implying that these segments are collinear. This means that the center of gravity is located at the boundary of the triangle OPQ and the rollover is imminent, as it is shown in Fig. 4.
Thus, the maximum turning angle αmax can be evaluated in the form
2MS2 F- αmax = tan-1 A
S F+ 2M
S +1-S2 2 4M2 A2
(7)
A
by considering F =
; S = B
2L-2M-C (8)
Figure 3. Design solutions for the steering ability: a) a scheme of the robot containing both solutions; b) turning wheels
solution; c) turning legs solution.
Figure 4. A scheme for the determination of the maximum allowed rotation angle.
Results of this analysis can be summarized as follows:
the turning wheels solution has a limited maximum angle αmax that results in a low maneuverability of the vehicle. This does not happen when the steering system based on turning legs is considered, so that αmax can be increased up to 90 degrees.
4. Design and Simulation of the Leg-Wheel Hybrid Robot
Regarding to mobile robots, light and simple control architectures can be considered when the system has a reduced number of DOFs and reduced mechanical complexity14. Furthermore, basic considerations for a leg design can be outlined as follows: the leg end-point trajectory should approximate a straight-line for the support phase; the leg should be manufactured with commercial components having suitable DOFs to ensure requested motion capability. According to those basic requirements a leg has been designed by considering robustness, reconfigurability17, light weight, reduced number of DOFs as basic characteristics for an easy- operation. Furthermore, the mechanical design has been conceived by using a linkage architecture in order to build a low-cost prototype. Indeed, aluminum has been selected because of its lightness and easy manufacturing. The mechanical design of the robot is the main issue of a project with the aim to obtain a simple system, that is able to walk in several environments. Indeed, this prototype is intended to be used for such applications in which if it gets destroyed it can be easily replaced. The prototype consists of a biped module, whose two active legs are described in Section 2, a DC motor for actuation, and two passive wheels.
Additionally, the prototype should be provided by a steering system.
Two solutions have been proposed for the steering system providing numerical simulations. These simulations allow to compare the performances of the hybrid robot to get the minimum radius of rotation preventing also overturning. In the simulations the robot starts to walk on straight path. From t = 2s to t = 3s the additional DOF is activated (turning wheels or legs, depending by the solution) keeping the configuration and movement until a full turn is completed. The time required to execute a full rotation is proportional to the length of the travelled path.
In a first series of simulations reported in Fig. 5a), the hybrid robot changes its direction by the turning wheels solution. In particular, Fig.5a) shows the trajectory of point H, which is the midpoint of the axis of rotation of the wheels in Fig. 3, when the shaf is rotated with respect to the wheel chassis by an angle of 60 deg. The radius of the generated trajectory during the simulation
was 896 mm. This path was followed with an average speed of 349 mm/s, taking 10.8 seconds to complete a full rotation of the chassis. The turning radius is large leading to a limited maneuverability of the system. This radio cannot be further reduced because of the risk of overturning, since the center of mass of the vehicle could fall out of the support polygon.
The second set of simulations have been performed by using the turning legs solution. Figure 5b shows the trajectory of the point H when the legs are rotated by 60 deg. The radius of the generated trajectory during the simulation was 372 mm, this path was followed with an average speed of 129 mm/s, taking 20.5 s to complete a full rotation of the chassis.
Figure 5 shows also snapshots of the simulations to facilitate the understanding of the proposed solutions.
In these figures the positions of the points H and K are marked for 6 different configurations at given times for both solutions.
a)
b)
Figure 5. Snapshots of the simulations of the steering systems: a) turning wheels solution; b) turning legs solution.
It is worth noting that with the turning legs solution a smaller value of the radius of the generated trajectory can be obtained, if compared to the turning wheels system.
A drawback is related to the time required to complete a full rotation, which is considerably high for the turning legs. An important advantage of the tuning wheel is the load capacity of the robot, which is considerably higher than the counterpart, and simplicity of realization. Therefore, according to the above mentioned considerations, the design solution of the turning wheels has been adopted for the construction of a prototype.
The leg-wheel mobile robot design and its steering system are shown in Figs. 6 and 7.
In general, the basic aim of a steering system is to ensure that the wheels are pointing in any desired direction. This can be obtained by a series of linkages, rods, pivots and gears. One of the fundamental parameters to consider is that of caster angle, each wheel is steered with a pivot point ahead of the wheel;
this makes the steering tend to be self-centering towards the direction of travel.
A simple approximation to perfect Ackermann steering geometry may be generated by a linkage. In particular, according to the low-cost design philosophy, a steering system based on a four-bar linkage has been considered for the design of the 2 DOF hybrid robot, as shown in Fig. 6. The steering linkages connecting the steering box and wheels usually conforms to a variation of Ackermann steering geometry, taking into to account for the fact that in a turn, the inner wheel is actually travelling a path of smaller radius than the outer wheel, so that the degree of toe suitable for driving in a straight path is not suitable for turns.
The mechanism has been synthesized according to the algorithm for the kinematic synthesis of mechanisms, which has been reported in [18]. In particular, an optimal value for the rotation angle was considered as it was obtained by the proposed models and reported simulations.
The designed steering system based on a four-bar linkage is shown in Fig. 7. The mechanism has been installed beneath the chassis of the robot. In particular, as regarding to the design and realization of the robot, each leg has been provided by suitable foot, which has been rigidly installed at the leg tip, for walking in both flat and rough terrains. In particular, in Fig. 8 simulations of the robot walking are given. They have been used to check the feasibility of the mechanical design solutions.
Several static and dynamic simulations have been run to test the robot stability during the walking on flat and sloped surfaces, in order to test the ability in overpass obstacles also.
The actuation is transmitted to the two active legs through a gear transmission system. The body of the mobile robot has been conceived in order to be able to carry batteries and a suitable PLC for operating the robot. Furthermore, it allows to a further installation of suitable sensors and acquisition system, according to the specific application.
Figure 6. A mechanical design of the robot.
a)
b)
Figure 7. A scheme of the steering system: a) 3D view;
b) bottom view
Figure 8. Simulation results on a flat surface.
5. Experimental Results
A prototype of the leg-wheel hybrid robot has been built for experimental validation. It is shown in Fig. 9. It has been built by considering such aspects that can be outlined as follows:
• modularity, considering future development of multi- leg reconfigurable systems19 ;
• autonomy, in the future the system will carry batteries and other specific sensors for collision avoidance and the specific application;
• low-cost and easy-in-use.
Several parts in the prototype are easily available low- cost commercial components. Body and legs have been made by aluminum with the aim to have a limited weigh and also to facilitate the manufacturing of the parts. The actuation system consists of a DC motor installed on the body of the hybrid robot. It drives the two legs through a gear transmission system, its power is 30 W and its torque is 13.3 Nmm. According to these values the traction force on the leg-tip ranges from 150 to 250 N for the support phase. Another DC motor is used to drive the steering system (power 13 W).
During the walking the prototype has always a leg and two wheels in contact with the ground. The mass distribution and body shape give that the projection of the center of gravity always in the area that is limited by the contact points with the ground.
The velocity is constant during the walking on flat
terrain, and depends also by the friction between foot and ground. The walking sequence in Fig. 10 has been obtained in an outdoor experiment on rough and sloped terrain. Characteristic dimensions of the prototype are 0.500 x 1.000 x 0.400 m and mass of 9 kg (batteries not included). The step of the robot has a maximum height of 0.03 m and a length of 0.16 m, and its shape allows the prototype to walk over terrains of various nature.
The prototype has been tested by walking forward and backward on flat terrain. It was tested also in a slope of about 20 deg. The backward walk has been obtained more efficiently than in the case of pulling walk mode.
The difference can be explained by considering the position of the center of mass and friction of the floor plane. Maximum velocity is 0.07 m/sec. It decreases depending on the slope of the ground, because of the masses distribution, and on terrain nature. Maximum velocity is limited, this is because the prototype is intended to be use for exploration or surveillance, indeed very high velocity is usually not required, since the robot could be used for acquiring data from the environment. Nevertheless, by modifying the actuation system it is possible to reach higher velocity of walking.
The prototype has been designed in order to have a low- cost, easy operating system able to walk on several operating conditions
Figure 9. A prototype of the 2 DOF hybrid walking robot.
6. Conclusion
In this paper a prototype of 2 DOF leg-wheel walking robot is proposed. The design philosophy we have chosen deals with relatively low-cost design, in terms of manufacturing and simplicity in use. Therefore, a mechanism with reduced DOFS can be manufactured and controlled rather easily reducing both costs and complexity. This kind of robot is intended to be used in such environments for which if the it gets lost or hardly damaged (e.g. during exploration for demining, or in nuclear plants) it can be easily replaced. Experimental results have been obtained successfully by testing the prototype over several terrains.
Figure 10. Experiments on irregular surface with a slope.
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