Realization Energy Optimization of Complete Path Planning in Differential Drive Based Self-Reconfigurable Floor Cleaning Robot
Abstract
:1. Introduction
2. hTetro-Reconfigurable Floor Cleaning Robot
2.1. hTetro Kinematic Design with Differential Drive Mechanism
2.2. Representation of hTetro in a Workspace
3. CCPP Framework for hTetro by Tilling Theory
3.1. Localization of hTetro Blocks for Tileset of Workspace
Algorithm 1: Finding optimal blocks location for tileset. |
1 Function LOCATIONS OF BLOCKS ASSIGNMENT{workspace, tiling set}: 2 workspace{} 3 i ←1, j ←1, t ←1 4 for all i, i ←1, do 5 for all j, j ←1, do 6 if is COM of tiling pattern t then 7 if tiling pattern t is asymmetrical shape then 8 Assign: blocks locations of t according Figure 8 9 else if t is symmetrical shape then 10 Do: transformation from tile to tile t (note that orientation of hTetro is defined by Figure 4) 11 Find: tiling pattern blocks as in Figure 10 which yields the similar location in orientation with the orientation after transformation (note that orientation of hTetro is defined by Table 4) 12 Assign: blocks locations of t according Figure 9 13 end 14 end 15 end End Function |
3.2. Local Navigation Weight Function
3.3. Optimization of Trajectory
4. Experimental Results
4.1. Simulation Environment
4.2. Real Environment Testbed
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Terms | Meaning |
---|---|
Mass of the module i where | |
Center of mass of module i where at waypoint s | |
Center of the mass of the robot at waypoint s | |
Center of the mass of the robot at waypoint s after transformation | |
Center of the mass of the robot at next destination waypoint d | |
Function to calculate the total distance translated by all modules towards the desired target location | |
The required angle to perform the transformation by module i where | |
Turning radius for the module in Single Module Locomotion (SML) | |
Turning radius for the outermost module in Double Module Locomotion (DML) | |
Function to calculate the total distance travelled by all module to perform transformation | |
Magnitude of the distance between center of the mass of each module and that of the robot where at waypoint s | |
Desired orientation of the robot at waypoint d with respect to the global frame | |
Current orientation of the robot at waypoint s with respect to the global frame | |
Orientation offset of the robot after tramsfomation from waypoint s to waypoint d as in Table 4 | |
Function to calculate the total distance travelled by all modules towards the desired orientation | |
Total travelled distance for a pair n by the robot from one source waypoint to next destination waypoint performing transformation, translation, orientation correction |
O Shape A B C D | I Shape A B C D | L Shape A B C D | Z Shape A B C D | T Shape A B C D | J Shape A B C D | S Shape A B C D | ||
---|---|---|---|---|---|---|---|---|
O Shape | 0 0 0 0 | 0 0 | (,) 0 0 | 0 (,) | 0 0 | (,) 0 | (,) 0 0 | |
I Shape | 0 0 | 0 0 0 0 | 0 0 0 | 0 0 | 0 (,) | (,) 0 | (,) 0 0 | |
L Shape | (,) 0 0 | 0 0 0 | 0 0 0 0 | 0 0 0 | 0 ( ) | 0 0 0 | 0 0 | |
Z Shape | 0 (,) | 0 0 | 0 0 0 | 0 0 0 0 | 0 | 0 0 | 0 | |
T Shape | 0 0 | 0 ( ) | 0 | 0 | 0 0 0 0 | 0 | (, ) 0 | |
J Shape | (,) 0 | (,) 0 | 0 0 0 | 0 0 | 0 | 0 0 0 0 | 0 0 0 | |
S Shape | (,) 0 0 | (,) 0 0 | 0 0 | 0 | 0 (,) | 0 0 0 | 0 0 0 0 |
O Shape A B C D | I Shape A B C D | L Shape A B C D | Z Shape A B C D | T Shape A B C D | J Shape A B C D | S Shape A B C D | ||
---|---|---|---|---|---|---|---|---|
O Shape | 0 0 0 0 | 0 0 | (,) 0 0 | 0 (,) | 0 0 | (,) 0 | (,) 0 0 | |
I Shape | 0 0 | 0 0 0 0 | 0 0 0 | 0 0 | 0 (,) | (,) 0 | (,) 0 0 | |
L Shape | (,) 0 0 | 0 0 0 | 0 0 0 0 | 0 0 0 | 0 | 0 | 0 (,) | |
Z shape | 0 (,) | 0 0 | 0 0 0 | 0 0 0 0 | 0 | 0 0 | 0 | |
T Shape | 0 0 | 0 (,) | 0 | (,) 0 | 0 0 0 0 | 0 | 0 (,) | |
J Shape | (,) 0 | (,) 0 | 0 | 0 0 | 0 | 0 0 0 0 | 0 0 0 | |
S Shape | (,) 0 0 | (,) 0 0 | 0 (,) | 0 | 0 (,) | 0 0 0 | 0 0 0 0 |
O Shape | I Shape | L Shape | Z Shape | T Shape | J Shape | S Shape | ||
---|---|---|---|---|---|---|---|---|
O Shape | 0 | 0 | ||||||
I Shape | 0 | |||||||
L Shape | 0 | 0 | 0 | 0 | ||||
Z shape | 0 | 0 | ||||||
T Shape | 0 | 0 | ||||||
J Shape | 0 | 0 | 0 | |||||
S Shape | 0 | 0 |
Method | Euclidean Distance | Proposed Cost Weight | Trajectory Generating Time |
---|---|---|---|
Zigag | 3814.12 | 4072.19 | 0.012 |
Sprial | 3612.21 | 3821.18 | 0.155 |
Greedy search | 2994.52 | 3791.92 | 30.24 |
Method [22] | 2943.32 | 3688.21 | 1.150 |
Propsed method GA | 3122.56 | 2968.95 | 1.158 |
Propsed method ACO | 3125.52 | 2933.19 | 1.166 |
Coefficient Values | Meaning | Cost Weight Action | Cost Weight All Actions | Energy (Ws) on Real Workspace |
---|---|---|---|---|
Only transformation | 1192.35 | 1239.29 | 24.32 | |
Only translation | 1198.165 | 1259.35 | 25.34 | |
Only orientation | 1201.32 | 1279.91 | 28.32 | |
transformation and translation | 1182.251 | 1256.80 | 25.61 | |
Only translation and orientation | 1198.31 | 1218.83 | 24.25 | |
All three actions | 1209.19 | 1209.19 | 22.03 |
Workspace | Tiling Set | Cost Weight |
---|---|---|
6 × 6 | Tileset 1: O, I, J, L | 1209.19 |
Tileset 2: J, O, L, S, N | 1189.26 | |
8 × 7 | Tiling set 1: I, L, J | 1502.16 |
Tileset 2: I, O, L, T | 1558.44 | |
11 × 11 | Tileset 1: J, T, S, L | 2933.69 |
Tileset 2: O, I, L, J | 2892.68 |
Cost Weight | Trajectory Generating Time | |
---|---|---|
chromosome = 30, mutation probability = 0.01 | 3176.59 | 1.22 |
chromosome = 30, mutation probability = 0.05 | 3371.18 | 1.31 |
chromosome = 30, mutation probability = 0.1 | 3381.32 | 1.340 |
chromosome = 100, mutation probability = 0.01 | 2988.21 | 1.150 |
chromosome = 100, mutation probability = 0.05 | 2998.95 | 1.662 |
chromosome = 100, mutation probability = 0.1 | 2968.95 | 1.580 |
Cost Weight | Trajectory Generating Time | |
---|---|---|
number of ants = 50, evaporation probability = 0.1 | 3372.29 | 1.412 |
number of ants = 50, evaporation probability = 0.5 | 3321.68 | 1.555 |
number of ants = 50, evaporation probability = 0.9 | 3211.97 | 1.740 |
number of ants = 100, evaporation probability = 0.1 | 3688.21 | 1.850 |
number of ants = 100, evaporation probability = 0.5 | 2958.95 | 1.762 |
number of ants = 100, evaporation probability = 0.9 | 2933.19 | 1.660 |
Method | Cost Weight | Running Time (s) | Power (W) | Energy (Ws) |
---|---|---|---|---|
Zigzag | 1412.35 | 147.09 | 0.285 | 41.92 |
Spiral | 1391.19 | 146.42 | 0.257 | 40.27 |
Greedy search | 1352.19 | 136.92 | 0.238 | 32.59 |
Method [22] | 1301.25 | 129.87 | 0.198 | 25.71 |
Proposed method GA | 1216.59 | 122.92 | 0.185 | 22.74 |
Proposed method ACO | 1209.19 | 121.04 | 0.182 | 22.03 |
Transform | O to O | O to J | J to J | J to L | L to L | L to I | I to I | I to O |
---|---|---|---|---|---|---|---|---|
Navigation sequence | 1 to 3 | 3 to 2 | 2 to 7 | 7 to 6 | 6 to 9 | 9 to 4 | 4 to 5 | 5 to 8 |
Consumed energy (Ws) | 1.82 | 3.51 | 2.11 | 3.16 | 2.25 | 3.32 | 2.31 | 3.55 |
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Le, A.V.; Ku, P.-C.; Than Tun, T.; Huu Khanh Nhan, N.; Shi, Y.; Mohan, R.E. Realization Energy Optimization of Complete Path Planning in Differential Drive Based Self-Reconfigurable Floor Cleaning Robot. Energies 2019, 12, 1136. https://doi.org/10.3390/en12061136
Le AV, Ku P-C, Than Tun T, Huu Khanh Nhan N, Shi Y, Mohan RE. Realization Energy Optimization of Complete Path Planning in Differential Drive Based Self-Reconfigurable Floor Cleaning Robot. Energies. 2019; 12(6):1136. https://doi.org/10.3390/en12061136
Chicago/Turabian StyleLe, Anh Vu, Ping-Cheng Ku, Thein Than Tun, Nguyen Huu Khanh Nhan, Yuyao Shi, and Rajesh Elara Mohan. 2019. "Realization Energy Optimization of Complete Path Planning in Differential Drive Based Self-Reconfigurable Floor Cleaning Robot" Energies 12, no. 6: 1136. https://doi.org/10.3390/en12061136