Obstacle avoidance planning of space manipulator endeffector based on improved ant colony algorithm
 Dongsheng Zhou^{1}Email author,
 Lan Wang^{1} and
 Qiang Zhang^{1}Email author
Received: 20 January 2016
Accepted: 13 April 2016
Published: 23 April 2016
Abstract
With the development of aerospace engineering, the space onorbit servicing has been brought more attention to many scholars. Obstacle avoidance planning of space manipulator endeffector also attracts increasing attention. This problem is complex due to the existence of obstacles. Therefore, it is essential to avoid obstacles in order to improve planning of space manipulator endeffector. In this paper, we proposed an improved ant colony algorithm to solve this problem, which is effective and simple. Firstly, the models were established respectively, including the kinematic model of space manipulator and expression of valid path in space environment. Secondly, we described an improved ant colony algorithm in detail, which can avoid trapping into local optimum. The search strategy, transfer rules, and pheromone update methods were all adjusted. Finally, the improved ant colony algorithm was compared with the classic ant colony algorithm through the experiments. The simulation results verify the correctness and effectiveness of the proposed algorithm.
Keywords
Background
A space manipulator system is composed of system body (satellite) and its onboard manipulator. Since the manipulator system with gas thruster can fly or float free in the microgravity space environment, which expands the working space for the manipulator, so the manipulator system could instead astronauts engaged in a variety of extravehicular activities. Path planning of the manipulator system will become one of the main research directions in the area of space in the future (Yoshida and Wilcox 2008). In the space environment, space debris and cabin peripheral testing devices have the potential to be obstacles for space manipulator in the process of onorbit operation, and the collisions occurred between the manipulator and the obstacles will not only interfere with onorbit operation to complete the task, but also do harm to the manipulator system and operation personnel. Therefore, the obstacle avoidance path planning of space manipulator has very important research significance.
The main idea of the obstacle avoidance planning is designing an optimal path which can avoid all obstacles and meet certain targets from the starting point to the target point. For the path planning problem, a number of methods have been addressed, such as Cspace method (Ping et al. 2009), A* search method (Kala et al. 2010), the improved artificial potential field method (Liu and Zhang 2014), neural networks (Duguleana et al. 2012) and so on, but they all have certain limitations. Cspace method needs large computation. The calculation is more time consuming than the response of the manipulator which has limited its range of application in the area of the practical obstacle avoidance. Since the computational amount of A* search method will increase sharply with the increase of space dimension, it is difficult to satisfy its time and space requirements. The improved artificial potential field method is very suitable for dealing with dynamic obstacles, but it is easy to fall into local minimum point. During the process of searching path, the neural network method was easy to lose information. This caused it is difficult to find a feasible path to meet the constraints in a complex environment.
Ant colony algorithm has strong robustness and ability of distributed computing, and it is easy to be combined with other methods, but it also has some defects, such as slow convergence speed, easily falling into local optimum. In this paper, firstly we establish models for the space manipulator and the environment, and then transform the search strategy, transfer rules (Hao and Wang 2010) and pheromone update methods to improve the ant colony algorithm, and finally the improved ant colony algorithm is used to search the better obstacle avoidance path. Using this method, manipulator endeffector can avoid all the obstacles smoothly and its motion path is shorter than the path obtained by the basic ant colony algorithm.
Models of manipulator and environment
DH parameters of system
i  \(\alpha_{i  1}\)  \(a_{i  1}\)  d _{ i }  θ _{ i } 

1  \( \pi /2\)  0  d _{1}  θ _{1} 
2  \(\pi /2\)  0  0  θ _{2} 
3  \( \pi /2\)  0  d _{3}  θ _{3} 
4  \(\pi /2\)  0  0  θ _{4} 
5  \( \pi /2\)  0  d _{5}  θ _{5} 
6  \(\pi /2\)  0  0  θ _{6} 
7  0  0  d _{7}  θ _{7} 
Quality characteristics of space manipulator
B _{0}  B _{1}  B _{2}  B _{3}  B _{4}  B _{5}  B _{6}  B _{7}  

m (kg)  1146.342  3.692  60.416  3.678  35.654  3.461  2.624  0.114 
l (m)  0.85  0.13  1.5  0.12  1.24  0.22  0.07  0.01 
I _{ xx } (kg m^{2})  291.077  0.013  13.556  0.012  1.235  0.061  0.066  0 
I _{ yy } (kg m^{2})  536.263  0.005  2.274  0.010  7.309  0.028  0.004  0 
I _{ zz } (kg m^{2})  669.647  0.015  15.756  0.005  6.104  0.035  0.004  0 
The comments of the symbols
System CM  The system’s center of gravity 

\(\sum {\text{I}}\)  The inertial coordinate system 
B _{0}  Base of the system 
B _{ i } (i = 1,2…,7)  The ith link 
\(J_{i}\)  The ith joint 
\(C_{i}\)  Gravity center of B _{ i } 
\({\varvec{a}}_{i}\)  Position vector from J _{ i } to C _{ i } 
\({\varvec{b}}_{i}\)  The distance from C _{ i } to \(J_{i + 1}\) 
\({\varvec{b}}_{0} \in {\mathbf{R}}^{3}\)  Position vector from CM of base to joint 1 
\({\varvec{r}}_{b} \in {\varvec{R}}^{3}\)  Position vector of the center of mass (CM) of base 
\({\varvec{r}}_{i} \in {\varvec{R}}^{3} \left( {i = 1,2, \ldots ,7} \right)\)  Position vector of CM of link \(i\) 
\({\varvec{r}}_{g} \in {\varvec{R}}^{3}\)  Position vector of the system 
\({\varvec{r}}_{e} \in {\varvec{R}}^{3}\)  Position vector of endeffector 
\({\varvec{p}}_{i} \in {\varvec{R}}^{3}\)  Position vector of joint \(i\) 
\({\varvec{p}}_{i}\)  Position vector of \(J_{i}\) 
\(\alpha_{i  1}\)  The link corner of manipulator 
\(a_{i  1}\)  The length of common vertical line from the joint shaft \(i  1\) to i 
d _{ i }  The link offset 
θ _{ i }  The ith joint angle 
\({\varvec{\varTheta}} \in {\varvec{R}}^{n}\)  Joint angle vector 
m _{ i }  Mass of link i 
l _{ i }  Length of the ith link 
I  Movement inertia of the links 
Kinematics equation of space manipulator
Expression of valid path in space environment
Obstacle avoidance planning based on improved ant colony algorithm
Inspired by the fact that ants always find a shortest path between the food and the nest during the foraging process, M. Dorigo proposed ant colony algorithm (Dorigo et al. 1996). Ant colony algorithm has many advantages, but there are some defects, such as high complexity, easy to fall into local optimum. In order to obtain the better obstacle avoidance path, the search strategy, transition rule and pheromone updating method in classical ant colony algorithm are improved in this paper.
Visual area
In this paper, we take x axis for the main direction of path planning and set the maximum transverse and longitudinal moving distance for ants (Feng et al. 2011). Thus, there is a visible area when the ants search the next node. This area plays the role of simplifying the search space and improving the search efficiency of ant colony algorithm.
Fitness function
Search strategy

Step 1: Determine the set of feasible points in the plane \(\prod_{i + 1}\).

Step 2: Calculate the heuristic information value \(H_{a + 1,u,v}\) of the set of feasible points according to the formula (4).

Step 3: Calculate the selection probability \(p\,\left( {i + 1,u,v} \right)\) at any point \(\left( {i + 1,u,v} \right)\) within the plane \(\prod_{i + 1}\):

$$p\left( {i + 1,u,v} \right) = \left\{ {\begin{array}{ll} \frac{\tau_{a + 1,u,v} H_{a + 1,u,v}} {\sum (\tau_{a + 1,u,v} H_{a + 1,u,v})} & {at\,feasible\,points} \\ 0 & {others} \\ \end{array} } \right.$$(9)

where, \(\tau_{a + 1,u,v}\) is the pheromone of point \(p\,\left( {a + 1,u,v} \right)\) in the plane \(\prod_{i + 1}\).

Step 4: Select the points in plane \(\prod_{i + 1}\) using the roulette wheel method on the basis of the selection probability of each point.
Transition probability
The probability value is computed by formula (9) during the process that ants search the obstacle avoidance path, and the node with the highest probability is selected as the next node. Due to the fact that ant colony algorithm is easy to fall into local optimum, the chosen node with high probability may not be the optimal solution, if the size of problem is large, it is more difficult to find the optimal solution (Hao and Wang 2010). In addition, if transfer probability is only obtained by using the (9), the algorithm will lose randomness and some good solutions will be ignored. Then, the consequence is that the global optimal solution is wrong. Therefore, the method of combining random and deterministic probability is adopted to select the nodes.
Updating pheromone
Steps of the algorithm

Step1: Initialization. The ants whose number is \(m\) are placed in the start point, setting iteration counter \(N_{c} = 0\), the maximum number of iterations \(N_{c{\rm max}}\), the number of ants \(N\), attenuation coefficient and update coefficient of the pheromone.

Step2: Ants search path. Search the next point according to formula (9) and (10), at the same time, record the path that ants have walked and update the local pheromone according to the formula (11).

Step3: To determine whether the target point is reached, then go to Step4, otherwise turn to Step2.

Step4: Update the total length of path. If the new path is shorter than the length of the known optimal path, we will replace the original optimal path with a new path.

Step5: Update the global pheromone for the updated path base on (12) and (13).

Step6: \(N_{c} = N_{c} + 1\), if \(N_{c} \le N_{c{\rm max} }\), then turn to Step2, otherwise put out the optimal path \(p\).
Simulation results
In this paper, the space manipulator with seven degrees of freedom is used for path planning about obstacle avoidance, for the convenience of theoretical research, the endeffector is only considered instead of the whole manipulator system.
Parameters setting of improved ant colony algorithm
Size of population  Decay coefficient of pheromone  Update coefficient of pheromone  Number of iterations  Coefficient K 

20  0.9  0.2  100  100 
Comparisons between ant colony algorithm and improved ant colony algorithm
Average fitness (m)  Average time (s)  Optimal fitness (m)  

Ant colony algorithm  62.1348  9.9841  58.9486 
Improved ant colony algorithm  55.2767  9.6831  50.7498 
The idea that choosing the next node with probability is similar to the greedy algorithm, they all consider the local optimal, but the ant colony algorithm considers the distance from the next node to the target, which can avoid falling in local optimum.
The fitness obtained by improved ant colony algorithm is smaller than ant colony algorithm, that is to say, the obstacle avoidance path achieved by improved ant colony algorithm is shorter than ant colony algorithm; Ant colony algorithm reaches the optimal fitness value close to 80 iterations, while improved ant colony algorithm only need more than 60 iterations, which shows that the convergence rate of improved ant colony algorithm is faster than ant colony algorithm; From the point of the whole running time, the average time of improved ant colony algorithm is shorter than ant colony algorithm. The above results show that the avoidance effect obtained by the presented algorithm is more effective than the standard ant colony algorithm for manipulator endeffector.
Conclusions
In this paper, an improved ant colony algorithm was presented and used for to plan the obstacle avoidance path to avoid the collisions between the space manipulator and obstacles when the manipulator executes the onorbit service. The transfer rules, pheromone update method and search strategy of the ant colony algorithm were discussed and improved. Compared with the standard ant colony algorithm, experiments show that the presented algorithm has many advantages: the efficiency of path planning is increased, and the planned path is shorter and safer. Simulation results demonstrate the feasibility and effectiveness of this method.
Of course, there still exist many aspects that need to be studied deeply. And, it will be a challenge to deal with a more complexity obstacles layout or a dynamic unstructured environment which will be our next most important research point.
Declarations
Authors’ contributions
Lan Wang wrote this manuscript; Dongsheng Zhou and Qiang Zhang contributed to the method, direction, writing and content and also revised the manuscript. All authors read and approved the final manuscript.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 61425002, 61300015), the Program for Liaoning Innovative Research Team in University (No. LT2015002), the Program for Dalian Highlevel Talent’s Innovation, the Program for Technology Research in New Jinzhou District (No. KJCXZTPY20140012), and the Program for Liaoning Key Lab of Intelligent Information Processing and Network Technology in University.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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