Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005
HYBRID NAVIGATION FOR A CLIMBING ROBOT BY FUZZY NEURAL NETWORK AND TRAJECTORY PLANNING YONG JIANG 1,2, MING-YANG ZHAO1, HONG-GUANG WANG1, LI-JIN FANG1 1
Robotics Laboratory, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016 2 Graduate School of the Chinese Academy of Sciences, Beijing 100039, China E-MAIL:
[email protected],
[email protected],
[email protected],
[email protected]
In this paper, a hybrid navigation method for the autonomous control of a miniature climbing robot is presented. The method of navigation blends the optimality of the trajectory planning algorithm with the capabilities in expressing knowledge and learning of the fuzzy neural network. The actual task environment of the climbing robot is both known and dynamic. Therefore the trajectory planning is used to search roughly the optimal trajectories towards the goal based the priori data. Meanwhile, by the multi-sensor data fusion process, the fuzzy neural network is employed in dealing properly with the uncertain and dynamic situations. The experiment platform of the miniature climbing robot is also described in the paper. The properties of the hybrid navigation method are verified by the computer simulation.
intelligent control in many areas [7]-[10]. In this research, a hybrid method of sensor-based navigation, combining the FNN and the trajectory planning, is presented and applied to a miniature climbing robot. The organization of the paper is as follows. Section Ⅱ briefly describes the mechanical structure and locomotion modes of the miniature climbing robot. Section Ⅲ develops a model for multi-sensor data fusion used practically in the control system. Section Ⅳ presents the design of the five-layer FNN. Section Ⅴ proposes a hybrid method of navigation and analyses the results of simulations on the miniature climbing robot. Finally, section Ⅵ outlines the main conclusions of the work.
Keywords:
2.
Abstract:
Hybrid navigation; multi-sensor data fusion; fuzzy neural network; climbing robot
1.
Introduction
For mobile robots operating in an unknown and changing environment, moving without collision is one of the most challenging tasks of an autonomous, intelligent robot system. The artificial potential field (APF) method provides simple and effective motion planning to solve this problem. However, the APF has a major disadvantage that the local minimums can trap a robot before reaching its goal. Improvements of APF method, such as the superquadratic potential [1], can avoid the local minimums but the calculation cost is increased because of the computational complexity. Also, the solutions employing different search techniques, including best-first [2] and constrained-motion [3], are usually unreliable for on-line purpose. In real-time world systems, sensor-based motion control becomes essential to deal with model uncertainties and unexpected obstacles [4]-[6]. In addition, the fuzzy neural networks (FNN), with the capabilities in expressing knowledge and learning, are widely applied to realize
2.1.
Mechanical structure and locomotion modes Mechanical structure
The mechanical structure of the miniature climbing robot is designed as a bipedal robot with an under-actuated
DSP Controller
Motor 2 Joint 2 Motor 1
Joint 4
Joint 3
Leg 2
Leg 1
Joint 1
Foot 1
Motor 3
Joint 5
Foot 2
Figure 1. Climbing robot mechanism [11], which minimizes the number of motors without sacrificing the mobility. As shown in Figure 1, motors 1 and 3 independently drive joints 1 and 5,
0-7803-9091-1/05/$20.00 ©2005 IEEE 1069
Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 respectively; thereby adjusting the tilt angle of the suction feet 1and 2 so that the robot can grip the surface firmly. Motor 2 is responsible for controlling joints 2, 3 and 4, but not all of them simultaneously. Joints 2 and 4 are revolute joints providing steering capability of the feet relative to the legs. Joint 3 represents the prismatic motion of the legs that allows the robot expanding and contracting its legs. The under-actuated mechanism enables the robot to drive 5 joints using only 3 motors, thus reducing both the weight and the power consumption of the robot, achieving good balance between compactness and maneuverability. 2.2.
Fuzzy Neural Network
layer Comparing
Fusion computing
Estimating
layer
Classification ……
Preprocessing
Signal amplifier
layer
Filter circuit A/D conversion
Locomotion modes
……
The innovation in the design of the mechanical structure makes the climbing robot have the capability to switch between three locomotion modes, namely, translation mode, Spin-1 mode and Spin-2 mode, as in [11]. --Translation mode: In this mode, the joints 2 and 4 are prevented from rotating, thereby the rotation of motor 2 causes translation motion of the legs. --Spin-1mode: If the translation motion contracts beyond a certain range, the drive of motor 2 will allow the clock-wise rotation of foot 1 about joint 2. Meanwhile, leg 2 continues to contract and joint 4 is held fixed. --Spin-2 mode: If the translation motion extends beyond a certain range, the drive of motor 2 will allow the counter-clock-wise rotation of foot 2 about joint 4. Meanwhile, leg 1 continues to extend and joint 2 is held fixed. 3.
Control algorithm
Multi-sensor data fusion
Multi-sensor data fusion refers to the acquisition, processing and synergistic combination of information gathered by various knowledge sources and sensors to provide a better understanding of the phenomenon under consideration. Since data fusion was put forward in 70s last century, this research has acquired great achievements. Applications for it are widespread, both in military and civilian areas. Ref. [4] provides an overview of multi-sensor data fusion technology and its applications. When moving in a dynamic and uncertain environment, the miniature climbing robot can acquire the information of exterior and self states for robot navigation by multiple sensors. A model for the multi-sensor data fusion process is shown in Figure 2. The basic components of this model include sensor layer, preprocessing layer, and fusion computing layer. The functions for each block are briefly described next.
Sensor layer
Encoders
Pressure
Infrared
Hall
sensors
sensors
switches
Touch
sensors
Figure 2. Model for the data fusion process 1) Sensor layer: The pressure sensors monitor the pressure level inside the two suction cups to ensure that the robot feet grip the object surface firmly without leakage. The infrared sensors are used to measure the distance between the robot and the barriers. The hall switches are installed on each leg to discriminate different motion modes. The touch sensors affixed to the brim of the suction cups provide tactile feedback. The encoders are responsible for detecting the movement of each joint. 2) Preprocessing layer: The information from the sensor layer is modulated to suited digital signals by such hardware circuits as amplifier, filter and A/D conversion. 3) Fusion computing layer: This layer, a core of the model, consists of special fusion rules. Fusion computing, such as comparing, estimating, classification, etc, is based entirely on these rules. Touch sensor 1 Touch sensor 6
Touch sensor 2 Brim of the suction cup Touch sensor 3
Touch sensor 5 Touch sensor 4
Figure 3. Distribution of the six touch sensors Example: Consider the data fusion of the six touch sensors on a suction cup, as in Figure 3. Let P1 denote the probability of full contact between the foot 1 and the object surface, i.e.
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Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 6
∑T
i
P1 =
i =1
6
× 100%
(1)
Here Ti represents the state data of the touch sensor i ,
i = 1" 6 .
node in layer 3 is a rule node to represent the fuzzy rule. Each node in layer 4 represents a possible THEN part of fuzzy rule. The nodes in layer 5 carry out the defuzzification to get crisp values for output variables. 1) Layer 1: The input layer transforms the input vector
(
)
X = x1(0 )
x 2(0 ) " x n(0 ) into second layer directly. T
The ith node in this layer connects (2) In the control algorithm layer, the outputs of the multi-sensor data fusion are processed as the inputs of the model for the FNN. 4.
(0 )
variable xi , as a fuzzy language variable, has mi values. j
Let Ai ( j = 1, " , mi ) denote the jth language variable (0 )
Generally, a neural network has good learning abilities but is not suitable for expressing rule-based knowledge, while fuzzy logic is good at expressing approximate and quantitative knowledge but has poor learning abilities. In contrast to the pure neural network or fuzzy system, the FNN possesses both their advantages. It combines the capability of fuzzy reasoning in utilizing initial experiences and handling uncertain information and the capability of neural network in learning from process. Therefore the FNN systems are applied to many fields successfully [7]-[10]. In this paper, a FNN with a five-layer structure is used. xij(2)
( i = 1, " , n ), the ith output of layer 1. Each input
value of xi .
Fuzzy neural network
xi(1)
xi(0 ) to xi(1)
xk(3)
2) Layer 2: The fuzzification layer transfers the crisp values to membership degrees through membership functions. The layer consists of the term nodes, such as NB, NM, NS, Z, PS, PM, PB, etc. The activation function in each node serves as membership function. For each node in this layer, the input and output are represented in the form of Gaussian function (3), trapezium function, triangle function or Boolean function (4).
x
=e
(x
)
2 ()1 i − cij 2 σ ij
(3)
(1)
1 xi = x0 xij( 2) = (1) 0 xi ≠ x0 i = 1," , n , j = 1,", mi
xk(4)
x1(0)
( 2) ij
−
y1
Here cij and
σ ij are
(4)
the parameters of mean and standard (0 )
deviation of the jth Gaussian membership function of xi , respectively.
xn(0)
yr
Layer 1
Layer 2
Layer 3
Input
Fuzzification
Rule
Layer 4
3) Layer 3: Each node in the rule layer represents a possible IF part of a fuzzy rule. The node in this layer performs fuzzy AND operation. The functions of the layer are
Layer 5
OR Operation Defuzzification
Figure 4. Network structure of five-layered FNN
x k(3 ) = x1(i21 ) x 2(2i2) " x ni(2n)
4.1. Network structure The proposed five-layer FNN is shown in Figure 4, which consists of input, fuzzification, rule, OR operation and defuzzification layers. It performs the multiple inputs and multiple outputs. Nodes in layer 1 are input nodes that transmit input signals to the next layer directly. Nodes in layer 2 are linguistic term nodes treated as membership functions to express the fuzzy linguistic variables. Each
where i1 ∈ {1,
(5)
2, ", m1 } , i2 ∈ {1, 2, ", m2 } , n
" , in ∈ {1, 2, " , mn } , k = 1, " , m , m = ∏ mi . i =1
Thus, the output of node k in layer 3 is a product value of
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Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 all input to this node. 4) Layer 4: This is the OR operation layer. Each node in it represents a possible THEN part of fuzzy rule. Fuzzy OR operation is performed. The nodes of Layers 3 and 4 are fully connected. The functions in this layer are (4 )
xk =
x k(3) m
∑x
(3 )
k = 1,", m
pair.
′ ′ ′ D y l (k ) = y l1 (k )," , y lol (k ) (10) Step 5: Assign importance degree = (k ) to each data
′ ′ =(k ) = max D x1(0 ) (k ) ⋅ ⋅ ⋅ max D x n(0 ) (k ) (11) ′ ′ ⋅ max D y1 (k ) ⋅ ⋅ ⋅ max D y r (k )
(6)
k
Step 6: Construct fuzzy rules for each numerical data.
k =1
(0 )
5) Layer 5: The defuzzification layer, which performs the defuzzification of each node. The output signal can be evaluated as m
y l = ∑ wkl x k(4 )
(7)
k =1
k = 1,", m ,
l = 1,", r
(0 )
a
a
R(k): IF ( x1 is A1 1 and … and x n is An n ) b
b
THEN ( y1 is B1 1 and … and y r is Br r ) Step 7: Delete the conflict fuzzy rules. To solve the conflict rules, only the rule with the highest importance degree is selected. 4.3. Parameters learning
where wkl is the connecting weight between the kth node
All weights, except wkl between Layers 4 and 5, are
σ ij
in Layer 4 and the lth node in Layer 5.
assigned to one. The values cij and
4.2. Fuzzy rules
initial experiences and knowledge. The weights wkl are
The fuzzy rules are generated by using a simple method proposed in Ref. [12]. The main steps are as follows: Step 1: Determine the input and output (0 )
variables xi , i = 1, " , n and y l , l = 1, " , r . Step 2: Determine the membership function for each input and output variable. Step 3: Form the numerical data set. The kth numerical input and output data set, the training samples of FNN, can be formed as
x (0 )′ (k ), " , x (0 )′ (k ) → y ′ (k ), " , y ′ (k ) (8) 1 1 n r (0 )′ Step 4: For each input value xi (k ) and output ′ value y l (k ) , calculate the corresponding membership degree
′ ′ ( 2 )′ (k ) D xi(0 ) (k ) = xi(12 ) (k )," , xim i
(9)
are based on
updated to minimize the following error measure using gradient descent learning algorithm
E=
1 r ( y dl − yl )2 ∑ 2 l =1
(12)
where y dl and y l is the desired and actual output, respectively. The updating process can be expressed as
wkl (t + 1) = wkl (t ) − β where 0 < 5. 5.1.
∂E ∂wkl
(13)
β ≤ 1 is the learning rate of FNN.
Navigation of the climbing robot Hybrid navigation
The navigation system, which has to decide at every given moment where to move next, taking in consideration all the a priori information on the environment, the sensory data and its knowledge of the current position and orientation as well as the goal position, is a vital part of the design for an autonomous robot [13]-[15]. The methods for the navigation can be categorized as global if the algorithm
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Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 relies mostly on a priori information or local if its decision is taken using mainly the current sensor data. Generally, a global algorithm can find optimal trajectories according to various optimality criteria. However, it is unable to deal properly with dynamic situations. Another disadvantage is the need to have detailed knowledge of the environment. On the contrary, a local algorithm is good at these challenges but can not guarantee an optimal result. The navigation environment of the miniature climbing robot, such as the building, the pipeline, etc, is both known but also dynamic. In other words, we can get priori data of the task environment, whereas the uncertain and dynamic situations still exist. The solution presented here resolves this contradiction by using a hybrid navigation system composed of the trajectory planning and the FNN.
Prior data
Trajectory planning
The controller, serving as an under-stratum unit, drives the movement of the robot directly and gets the real-time information from the multiple sensors. The DSP programs are downloaded to the controller through the emulator. The host computer, intercommunicating with the DSP controller via RS-232 serial port, evaluates the super-stratum hybrid navigation algorithm.
Search optimal trajectories
Sensor information
Fuzzy neural network
Figure 6. Experiment platform of the climbing robot
Deal with uncertain
P(T) NT 1
dynamic situations
FT
0.5
Movement control
The composition and the way of functioning for the hybrid navigation system are shown in Figure 5. The trajectory planning is used to search roughly the optimal trajectories based on the priori data. The FNN is employed in generating the movement control. According to the real-time sensor feedback, the FNN is responsible for dealing with the uncertain and dynamic situations. At the same time, the intercommunion between the trajectory planning and the FNN orients the search process. Experiment and simulation
In order to acquire some data that will be processed in the simulations, it is necessary to build an experiment platform for the miniature climbing robot. Figure 6 shows the experiment platform of the miniature climbing robot, which consists of an on-board DSP controller, a SEED-XDS emulator and a host computer.
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P(P) LP 1
MP
HP
0.5 amount 0
Figure 5. Hybrid navigation system
5.2.
LT
1
2 3 4 5 6 0 0.1 0.2 0.8 0.9 input variable T(t) input variable P(t) (a) (b) P(D) ND MD FD 1
1
atm
0.5 0 10 20 40 50 input variable D(t) (c)
60
mm
Figure 7. Membership functions of the input variables (a)Touch Sensors T(t); (b) Pressure Sensor P(t); (c) Infrared Sensor D(t) In the simulated hybrid navigation of the miniature climbing robot, the A* algorithm is used for the trajectory planning. The main idea of this algorithm is to try to continue the route from the intermediary state which seems to be the most favorable, taking in consideration not only the cost of the way already made but also the estimate on the cost of the remaining part of the solution. Thereby, it can find the optimal route between an initial
Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 state and a goal state. The membership functions of the input variables to the FNN are shown in Figure 7. The fuzzy rules of the hybrid navigation for the simulation are as follows: R1: IF DL is ND and DM is ND and DR is FD THEN CR is MR. R2: IF DL is FD and DM is ND and DR is ND THEN CR is ML. R3: IF DL is ND and DM is FD and DR is ND THEN CR is MF. R4: IF DL is ND and DM is ND and DR is ND THEN CR is MB. ……
Local minimum
Obstacle
(c) Simulated route by the APF
(a) Simulated route by the APF 11
(d) Simulated route by the hybrid navigation Figure 8. Simulated results of the navigation to the miniature climbing robot
Goal
10 9 8
Here the CR denotes the movement direction of the climbing robot, and the MR, ML, MF, MB represents MOVE RIGHT, MOVE LEFT, MOVE FORWARD, MOVE BACK, respectively. Some simulations are performed to compare the hybrid navigation method with the APF approach, as in Figure 8. Figure 8 (a) and (b) show that in the same environment without any local minimum, the climbing robot can successfully reach the goal by either the APF approach or the hybrid navigation method. However, the lengths of the two routes in Figure. 8 (a) and (b) are unequal. The result by the hybrid navigation method is shorter than the one by the APF. In Figure 8 (c), the climbing robot is trapped by a local minimum though it
7 6 Y[m] 5 4 3 2 1
Start
0 1
2
3
4 5 X[m]
6
7
8
(b) Simulated route by the hybrid navigation
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Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005 avoids the collision with a traveling obstacle after using the APF. On the same conditions, Figure 8 (d) shows that the robot can not only avoid the collision with the traveling obstacle but also escape the local minimum by the hybrid navigation method.
[8] [9]
6.
Conclusions
In this paper, a hybrid navigation method, which blends the optimality of the trajectory planning algorithm with the capabilities in expressing knowledge and learning of the FNN, is presented and applied to the autonomous navigation of the miniature climbing robot. This navigation method can not only make good use of the prior data of the task environment, but also deal properly with the uncertain and dynamic situations. Moreover, based on the multi-sensor data fusion, it is simple and efficient to solve the local minimum problem by this technique. The results of the simulations show that the hybrid navigation method is useful for the real-time motion planning in both known and dynamic environment. The follow-up work includes optimizing the hybrid navigation method and verifying it in the real circumstance.
[10]
[11]
[12]
[13]
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