SCIENCE CHINA Information Sciences, Volume 61 , Issue 5 : 052204(2018) https://doi.org/10.1007/s11432-016-9115-2

Path planning for mobile robot using self-adaptive learning particle swarm optimization

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  • ReceivedDec 20, 2016
  • AcceptedMay 16, 2017
  • PublishedNov 15, 2017


As a challenging optimization problem, path planning for mobile robot refers to searching an optimal or near-optimal path under different types of constrains in complex environments. In this paper, a self-adaptive learning particle swarm optimization (SLPSO) with different learning strategies is proposed to address this problem. First, we transform the path planning problem into a minimisation multi-objective optimization problem and formulate the objective function by considering three objectives: path length, collision risk degree and smoothness. Then, a novel self-adaptive learning mechanism is developed to adaptively select the most suitable search strategies at different stages of the optimization process, which can improve the search ability of particle swarm optimization (PSO). Moreover, in order to enhance the feasibility of the generated paths, we further apply the new bound violation handling schemes to restrict the velocity and position of each particle. Finally, experiments respectively with a simulated robot and a real robot are conducted and the results demonstrate the feasibility and effectiveness of SLPSO in solving mobile robot path planning problem.


This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2013CB035503).


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  • Figure 1

    (Color online) The environment model for mobile robot path planning.

  • Figure 2

    The flowchart of SLPSO for mobile robot path planning.

  • Figure 3

    (Color online) The simulation environment for mobile robot path planning in Gazebo.

  • Figure 4

    (Color online) The path planning results of mobile robot using GA, PSO and SLPSO for different D. (a) Path length; (b) path collision risk degree; (c) path smoothness; (d) overall path cost.

  • Figure 5

    (Color online) The path planning results of mobile robot using GA, PSO and SLPSO for different D. (a) D= 5; (b) D= 10; (c) D= 15; (d) D= 20; (e) D= 25; (f) D= 30.

  • Figure 6

    (Color online) The overall path cost results of GA, PSO and SLPSO for mobile robot path planning with different D. (a) D= 5; (b) D= 10; (c) D= 15; (d) D= 20; (e) D= 25; (f) D= 30.

  • Figure 7

    (Color online) Turtlebot2 robot.

  • Table 1   Performance comparison of GA, DE, ACO, PSO, APSO and SLPSO on the 28 benchmark functions (=10)$^{\rm~a)}$
    Test function GA DE ACO PSO APSO SLPSO
    $~f_1(x)$ Mean $-$1.400E+03 $-$1.400E+03 $-$1.400E+03 $-$1.400E+03 $-$1.400E+03 $-$1.400E+03
    Std. Dev. 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
    $~f_2(x)$ Mean 1.058E+05 1.870E+05 6.546E+04 7.534E+04 3.504E+04 2.021E+04
    Std. Dev. 7.250E+04 6.670E+04 1.091E+04 3.549E+04 1.003E+04 1.073E+04
    $~f_3(x)$ Mean 9.445E+04 1.933E+05 2.358E+04 2.438E+03 $-$9.579E+02 $-$1.088E+03
    Std. Dev. 4.794E+04 1.137E+05 2.293E+04 2.320E+03 1.460E+02 1.070E+02
    $~f_4(x)$ Mean $-$1.088E+03 $-$1.089E+03 $-$1.096E+03 $-$1.097E+03 $-$1.092E+03 $-$1.099E+03
    Std. Dev. 6.435E+00 4.985E+00 3.040E+00 2.050E+00 3.931E+00 9.893E$-$01
    $~f_5(x)$ Mean $-$1.000E+03 $-$1.000E+03 $-$1.000E+03 $-$1.000E+03 $-$1.000E+03 $-$1.000E+03
    Std. Dev. 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
    $~f_6(x)$ Mean $-$8.902E+02 $-$8.902E+02 $-$8.986E+02 $-$8.996E+02 $-$8.986E+02 $-$8.999E+02
    Std. Dev. 6.174E+00 7.224E+00 3.224E$-$01 2.431E$-$01 1.207E+00 7.224E$-$02
    $~f_7(x)$ Mean $-$7.890E+02 $-$7.925E+02 $-$7.979E+02 $-$7.978E+02 $-$7.983E+02 $-$7.984E+02
    Std. Dev. 5.124E+00 6.404E+00 1.548E+00 1.127E+00 4.230E$-$01 7.652E$-$01
    $~f_8(x)$ Mean $-$6.797E+02 $-$6.797E+02 $-$6.797E+02 $-$6.797E+02 $-$6.799E+02 $-$6.799E+02
    Std. Dev. 6.645E$-$01 7.908E$-$01 2.192E$-$01 6.772E$-$01 7.953E$-$02 9.750E$-$02
    $~f_9(x)$ Mean $-$5.954E+02 $-$5.957E+02 $-$5.967E+02 $-$5.986E+02 $-$5.988E+02 $-$5.993E+02
    Std. Dev. 2.896E+00 3.742E+00 2.354E+00 1.112E+00 1.099E+00 6.444E$-$01
    $~f_{10}(x)$ Mean $-$4.988E+02 $-$4.986E+02 $-$4.995E+02 $-$4.994E+02 $-$4.997E+02 $-$4.998E+02
    Std. Dev. 1.082E+00 1.148E+00 4.528E$-$01 5.713E$-$01 1.365E$-$01 1.076E$-$01
    $~f_{11}(x)$ Mean $-$3.990E+02 $-$3.990E+02 $-$4.000E+02 $-$4.000E+02 $-$4.000E+02 $-$4.000E+02
    Std. Dev. 5.673E$-$01 4.893E$-$01 0.000E+00 0.000E+00 0.000E+00 0.000E+00
    $~f_{12}(x)$ Mean $-$2.791E+02 $-$2.741E+02 $-$2.881E+02 $-$2.901E+02 $-$2.930E+02 $-$2.970E+02
    Std. Dev. 1.287E+01 1.648E+01 7.256E+00 6.565E+00 4.876E+00 2.781E+00
    $~f_{13}(x)$ Mean $-$1.799E+02 $-$1.718E+02 $-$1.823E+02 $-$1.814E+02 $-$1.922E+02 $-$1.980E+02
    Std. Dev. 1.237E+01 1.653E+01 6.783E+00 5.981E+00 4.325E+00 1.911E+00
    $~f_{14}(x)$ Mean 1.476E+02 1.127E+02 $-$2.673E+01 $-$5.660E+01 $-$8.482E+01 $-$9.646E+01
    Std. Dev. 1.743E+02 1.013E+02 9.994E+01 3.657E+01 1.164E+01 3.206E+00
    $~f_{15}(x)$ Mean 8.286E+02 8.817E+02 5.737E+02 6.063E+02 4.089E+02 3.933E+02
    Std. Dev. 3.928E+02 1.968E+02 1.525E+02 1.872E+02 1.068E+02 2.368E+02
    $~f_{16}(x)$ Mean 2.010E+02 2.010E+02 2.008E+02 2.004E+02 2.007E+02 2.006E+02
    Std. Dev. 3.453E$-$01 4.196E$-$01 2.241E$-$01 1.044E$-$01 3.650E$-$01 2.005E$-$01
    $~f_{17}(x)$ Mean 3.118E+02 3.118E+02 3.115E+02 3.103E+02 3.104E+02 3.089E+02
    Std. Dev. 1.054E+01 1.024E+01 1.057E+01 6.562E$-$01 1.627E$-$01 5.873E+00
    $~f_{18}(x)$ Mean 4.301E+02 4.353E+02 4.299E+02 4.178E+02 4.085E+02 4.065E+02
    Std. Dev. 2.014E+01 1.497E+01 1.893E+01 4.534E+00 8.786E+00 5.287E+00
    $f_{19}(x)$ Mean 5.007E+02 5.007E+02 5.006E+02 5.004E+02 5.001E+02 5.002E+02
    Std. Dev. 3.092E$-$01 2.670E$-$01 2.143E$-$01 2.886E$-$01 9.650E$-$02 6.490E$-$02
    $f_{20}(x)$ Mean 6.035E+02 6.035E+02 6.032E+02 6.034E+02 6.010E+02 6.007E+02
    Std. Dev. 1.598E+00 1.201E+00 1.881E+00 4.194E$-$01 1.596E$-$01 1.895E$-$01
    $f_{21}(x)$ Mean 1.100E+03 1.100E+03 1.100E+03 1.100E+03 9.000E+02 8.000E+02
    Std. Dev. 1.414E+01 1.732E+01 0.000E+00 0.000E+00 0.000E+00 0.000E+00
    $f_{22}(x)$ Mean 1.143E+03 1.156E+03 1.027E+03 1.129E+03 8.206E+02 8.186E+02
    Std. Dev. 1.751E+03 1.842E+03 1.630E+03 1.515E+03 1.142E+03 1.072E+03
    $f_{23}(x)$ Mean 1.751E+03 1.842E+03 1.630E+03 1.515E+03 1.142E+03 1.072E+03
    Std. Dev. 5.929E+02 4.958E+02 3.631E+02 3.596E+02 8.774E+01 5.451E+01
    $f_{24}(x)$ Mean 1.215E+03 1.211E+03 1.210E+03 1.214E+03 1.206E+03 1.201E+03
    Std. Dev. 1.413E+01 2.822E+01 1.456E+01 1.370E+01 4.654E+00 9.401E+00
    $f_{25}(x)$ Mean 1.318E+03 1.315E+03 1.316E+03 1.312E+03 1.306E+03 1.301E+03
    Std. Dev. 7.124E+00 9.752E+00 9.832E+00 5.943E+01 4.831E+00 5.239E+002
    $f_{26}(x)$ Mean 1.510E+03 1.511E+03 1.400E+03 1.400E+03 1.314E+03 1.307E+03
    Std. Dev. 2.011E+02 1.096E+02 1.973E+02 9.513E+01 9.300E+01 8.615E+01
    $f_{27}(x)$ Mean 1.846E+03 1.850E+03 1.841E+03 1.636E+03 1.610E+03 1.601E+03
    Std. Dev. 2.115E+02 2.941E+02 1.836E+03 1.985E+02 8.800E+00 1.384E+01
    $f_{28}(x)$ Mean 1.700E+03 1.700E+03 1.700E+03 1.700E+03 1.700E+03 1.700E+03
    Std. Dev. 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
    a) “Std. Dev.” stands for the standard deviation.

    Algorithm 1 The SLPSO algorithm

    Initialize the parameters of SLPSO. Set the population size $N$, generate the initial particles with position and velocity, initialize the update frequency (${U_{\rm~f}}$), and set the generation counter k = 1.

    while $k~<~{\rm~Iter}_{\rm~max}$ do

    Calculate the inertia weight value by using (11).

    for ${i}=1$ to $N$

    if $k%~{U_{\rm~f}}==0$ then

    Update the selection ratio of each learning operator for particle i.

    end if

    Select the most suitable operator according to its selection ratio for particle i.

    Hand the boundary violation of velocity and position for particle i by using (16) and (17).

    Evaluate the objective function of particle i according to (7).

    Calculate the reward value, progress value and selection ratio of each operator of particle i for the iteration k+1 according to (12)–(15).

    if the updated particle i is better than its ${{\boldsymbol~X}_{\rm~pbest}^k}$ then

    Update ${{\boldsymbol~X}_{\rm~pbest}^k}$.

    end if

    if the updated particle i is better than ${{\boldsymbol~X}_{\rm~gbest}^k}$ then

    Update ${{\boldsymbol~X}_{\rm~gbest}^k}$.

    end if

    end for


    end while

  • Table 2   The path planning time (s) of GA, PSO, SLPSO for mobile robot path planning with different
    Algorithm D=5 D=10 D=15 D=20 D=25 D=30
    GA Mean 2.097E+00 1.338E+00 1.087E+00 9.368E$-$01 1.512E+00 5.422E+00
    Deviation 6.689E$-$01 1.276E$-$01 1.260E$-$01 2.524E$-$02 1.339E$-$01 1.230E+00
    PSO Mean 1.203E+00 1.220E+00 9.741E$-$01 6.257E$-$01 1.276E+00 3.193E+00
    Deviation 1.574E$-$01 1.264E$-$01 1.393E$-$02 2.473E$-$02 1.605E$-$01 1.265E+00
    SLPSO Mean 7.105E$-$01 7.771E$-$01 5.552E$-$01 3.226E$-$01 7.958E$-$01 1.957E+00
    Deviation 2.655E$-$02 1.479E$-$02 1.665E$-$02 1.629E$-$02 1.311E$-$02 1.554E$-$01
  • Table 3   The experiment results of GA, PSO, SLPSO for = 20
    Algorithm Length (m) Collision risk degree Smoothness (rad) Overall cost Running time (s)
    GA 2.259E+01 1.310E+01 7.761E+00 1.731E+01 3.388E+02
    PSO 2.180E+01 7.638E+00 4.298E+00 1.438E+01 3.269E+02
    SLPSO 2.051E+01 5.869E+00 3.516E+00 1.296E+01 3.077E+02

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