The communication demands of distributed model prediction control (DMPC) can overwhelm even advanced wireless communication technologies as agents must exchange a significant amount of information at least once per time step. To semantically reduce communication demands, this work employs encoder-decoder networks built around long-short term memory (LSTM) cells in a distributed optimization algorithm. Agents publish a reduced representation of a message and receivers reconstruct the original message upon reception. In tests with reduced communication using formations of mobile robots, trained networks retain satisfactory performance and work reliably under conditions overwhelming full communication. As the results show, the usage of LSTMs either allows unprecedented reconstruction accuracy or the usage of different prediction-horizon lengths without the necessity to retrain.
Figures & tables
Figure 1: Photograph of differential-drive mobile robots as a common example for nonholonomic mobile robots
Name
Encoder
Decoder
Communicate
SHRED [ 31 ]
LSTM
FFL
network output
Cell LSTM
LSTM
LSTM
cell state
LSTMP [ 32 ]
LSTM projected
LSTM projected
network output and cell state
LSTM+FFL
LSTM and FFL
LSTM and FFL
network output and cell state
LSTM+FFLH
LSTM
LSTM and FFL
network output
Table 1: Overview over the considered models providing their name, encoder and decoder architectures as well as the quantity they communicate
Figure 2: Semantic encoder-decoder structure: The encoded input sequence is published by robot i and received and decoded by the other robots in the formation j∈N\{i} .
Figure 3: Sketch of an encoder LSTM cell with optional projection layer
Figure 4: Overview over different LSTM architectures: (a) SHRED, (b) Cell LSTM, (c) LSTMP, (d) LSTM+FFL
Figure 5: Sketch of a decoder LSTM with an FFL. The FFL is only applied to the output of the last layer at τ=H . Note that the prediction sequence is recreated in reverse order from H to 0 in the decoder.
SHRED
Cell LSTM
LSTMP
LSTM+FFL
LSTM+FFLH
LSTM layer
2
2
2
2
2
Activation function
tanh
tanh/relu
tanh
Inner layer
25
Outer layer
35
batch size
1024
256
256
256
256
Validation Loss
0.00039
0.00093
0.00130
0.000574 / 0.000568
0.00059
Table 2: Hyperparameter settings with lowest mean validation loss over an epoch for the considered architectures.
Figure 6: Left: Trajectories of an example scenario with two robots for H=20 using no reduction (No red.) in the communication, SHRED, and LSTM+FFL communication reduction. The arrows in the left plot indicate the robot orientations for the task with full communication with the opacity increasing with time. Right: The corresponding value functions including all tested communication architectures for one robot.
Figure 7: Mean cost values at Tend of one robot for the test scenarios for all communication reduction techniques. The horizon lengths are connected with lines to improve readability.
Avg.
Max.
Min.
No reduction
1.66⋅10−15
9.38⋅10−14
<10−16
AE
3.12⋅10−10
9.89⋅10−9
2.03⋅10−11
SHRED
5.76⋅10−14
2.82⋅10−13
4.20⋅10−15
Cell LSTM
4.14⋅10−7
7.29⋅10−6
5.33⋅10−8
LSTMP
4.41⋅10−6
2.13⋅10−5
2.69⋅10−7
LSTM+FFL
8.89⋅10−9
4.90⋅10−7
2.99⋅10−11
Table 3: Overview of cost at Tend for H=20 .
Figure 8: Empirical cumulative distribution functions (CDFs) of error in y -direction for 60 random formation tasks with full and reduced communication.
Figure 9: Empirical cumulative distribution functions (CDFs) of error in y -direction for 60 random formation tasks with encoder-decoder LSTM-reduced communication for different H values.
H
Avg.
Max
Min
No reduction
18
2.29⋅10−14
2.26⋅10−12
<10−16
Cell LSTM
18
1.24⋅10−5
5.25⋅10−5
1.57⋅10−6
LSTMP
18
8.92⋅10−6
3.054⋅10−5
6.45⋅10−7
LSTM+FFL
18
1.11⋅10−8
6.55⋅10−8
4.28⋅10−10
LSTM+FFLH
18
1.50⋅10−8
2.34⋅10−7
9.81⋅10−10
No reduction
21
3.42⋅10−15
3.08⋅10−13
<10−16
Table 4: Mean, max, and min cost values at Tend of one robot for the test scenarios for all communication reduction techniques working for a variable horizon length. For each horizon length, the best performing reduction method is highlighted.
Figure 10: Setup for the numerical experiments
Figure 11: Left: Trajectories of an example parallel parking scenario with four robots using no reduction (No red.) in the communication, SHRED, and LSTM+FFLH communication reduction. Right: The value functions of one of the robots of a scenario with four robots.
Name
N
Tend
H
pˉ
Avg. info. received in %
No red.
8
800
20
3
98.97
SHRED
8
800
20
3
99.02
LSTM+FFLH
8
800
20
3
99.12
No red.
4
200
20
27
0.00
SHRED
4
200
20
27
98.29
LSTM+FFLH
4
200
20
27
90.70
Table 5: Average amount of communicated information received in percent on embedded hardware
Figure 12: Value functions for two experiments with N=8 and H=20
Figure 13: Left: Trajectories for one robot of an example scenario with H=25 and pˉ=10 using no reduction (No red.) in the communication and LSTM+FFLH communication reduction. Right: The value functions of one of the robots for all conducted experiment repetitions.
Institute for Dynamic Systems and Control, ETH Zurich, Switzerland · Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland