The motion of wheeled mobile robots is inherently based on their wheels' rolling capabilities. The assumption is that each wheel can rotate indefinitely, backwards or forward. This is the starting point for all motion control mechanisms of wheeled robots. In this paper, a new motion capability of differential mobile robots with limited wheel rotation capabilities is presented. The robot will be able to travel any distance and change its direction of movement even if its wheels can not rotate within more than a certain range of angles. The proposed solution is based on the bio-inspired controller principles used for modular and legged robots, in which oscillations are generated for achieving motion. A total of two oscillators, one per wheel, are enough to generate well-coordinated rhythms on the wheels to control the robot motion. The kinematics of this new type of mobile robot motion is presented, and the relation between the oscillator's parameters and the trajectory is studied. Experiments with real robots will demonstrate the viability of this new locomotion gait.

1. Motion Control of Differential Wheeled Robots
with Joint Limit Constraints
Speaker: Prof. Mohamed Abderrahim
J. Gonzalez-Gomez, J. G. Victores,
A. Valero-Gomez, M. Abderrahim
Robotics Lab
Carlos III University of Madrid, Spain
2011 IEEE International Conference on Robotics and Biomimetics
The Mövenpick Resort and Spa Karon Beach, Dec/2011
Phuket, Thailand

2. Motion Control of Differential Wheeled Robots with Joint Limit Constraints
Outline
1. Introduction
2. Swing principle
3. Kinematics
4. Experiments
5. Conclusions and future work
2011 IEEE International Conference on Robotics and Biomimetics

3. Rolling principle
● Rolling behaviour is inherent to wheels
● Wheels are assumed to rotate indefinitely in any direction
● All kind of known wheels rely on it:
Standard wheel Castor wheel Swedish wheel
Whegs Rotatory legs

4. Limited wheels
Wheels that cannot turn freely due to constraints
Limited by shape Limited by the environment
Ex. Broken wheel Ex. A Robot in a narrow path
Limit 1 Limit 2
Robot
Robot
Rot. angle

5. Locomotion with limited wheels
The problem:
● Imagine a robot with a broken wheel...
● Is it possible to achieve locomotion with
limited wheels?
● The rolling principle cannot be applied
● Another locomotion principle is necessary...
Applications:
● Improving the fault-tolerance of robots in critical missions
● Recovering the robot if wheels break
● Study and Develop new “locomotion gaits” with wheels

6. Our contribution: the swing principle
● Swing principle: Oscillating the wheels within the angle limits
● Differential robots with limited wheels can travel any
distance in some directions if applying the swing principle
Oscillations:
2π
φ1 =A sin( t +ϕ0 )+O
T
2π
φ 2= Asin ( t+Δ ϕ+ϕ0 )−O
T
Parameters: Amplitude (A), Offset (O)
Period (T), Phase difference (Δ ϕ)

7. Kinematics
● {Yi, Xi}: Global frame
● {XR,YR}: Robot frame
● (x,y, θ): Robot position and orientation
● r: Wheel's radius
● l: Distance from the wheels to the com
● Forward kinematics:
πr A 2π n
x=
˙ (C (0)+C (Δ ϕ))cos θ C ( x)=cos ( +ϕ0+ x)
T T
πrA
y=
˙ (C (0)+C (Δ ϕ))sin θ 2π n
T S ( x)=sin ( +ϕ0+ x)
r T
θ= (A S (0)− A S (Δ ϕ)+2O)
2l

8. Locomotion gait and trajectory
● The robot moves sideways
● Step: distance travelled per cycle
● When Δ ϕ=90 the step is maximum
● The step is proportional to the amplitude (A)
● The period determines the mean speed along the x axis

9. Trajectory orientation
● The robot can also move in different directions
●
The trajectory orientation depends on the offset (O)
● Limitations:
●The robot cannot move in all
the directions
●
Increasing O implies decreasing
the Amplitud (A)
● When A=0, there is no
locomotion

10. Experiments (I)
●A robot prototype with limited
wheels has been designed and built
● Wheels limited by shape
● Servos with mechanical limits
● IR led on the top for tracking the
trajectory

11. Experiments (II)
Video
● Real trajectory performed by the robot

12. Conclusions
● Swing principle: A new locomotion principle for robots with
limited wheels has been proposed
● It is based on wheels' oscillatory movement
●Despite the limited wheels, the robots can travel any distance in
some directions
Future work
●Test the swing principle with bio-inspired oscillators, such as CPGs
(Central Pattern Generators)
● Application to tracked robots
● Application to climbing slopes
● Application to wheelchairs

13. Motion Control of Differential Wheeled Robots
with Joint Limit Constraints
Speaker: Prof. Mohamed Abderrahim
J. Gonzalez-Gomez, J. G. Victores,
A. Valero-Gomez, M. Abderrahim
Robotics Lab
Carlos III University of Madrid, Spain
2011 IEEE International Conference on Robotics and Biomimetics
The Mövenpick Resort and Spa Karon Beach, Dec/2011
Phuket, Thailand