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This notebook documents the functions used to simulate the repeated updating of the state of the PID controller.
The general issues around the software interface between the VSA and multicopter components are discussed in Relation of VSA and multicopter simulation components.
The specific software design issues around the simulation of the PID controller are discussed in Structure of the VSA data flow graph implementation.
run_simulation()The function to run the simulation is defined as:
# Function to run an arbitrary simulation
run_simulation <- function(
input_df, # dataframe[n_steps, n_input_vars] - values of all input variables at all times
init_state, # dataframe[1, n_state_vars] - initial values of state variables used by f_update()
f_update # function(prev_state, input) - state update function, args are 1-row dataframes
) # value - dataframe[n_steps, n_input_vars + n_state_vars + 1]
# One row per time step
# One column for each input variable, state variable, and time (t)
{
# Apply the state update to tghe input values
state_df <- input_df %>%
base::split(seq(nrow(.))) %>% # split input into a list of 1-row data frames
purrr::accumulate( # accumulate list of simulated states
f_update,
.init = init_state
) %>%
purrr::discard(.p = seq_along(.) == 1) %>% # discard first element (initial state)
dplyr::bind_rows() %>% # convert list of time step states to a data frame
dplyr::bind_cols(input_df, .) %>% # add input variables
dplyr::mutate(t = 1:nrow(input_df), .before = everything()) # add time variable
}
# The input variables data frame is split into a list of one-row data frames
# because accumulate() requires it. The input variables could have been created
# in that format, but that's a much less convenient for general manipulation
# and the list of rows format is only required for accumulate().
# That's why the reformatting occurs on the fly in run_simulation().
# The time and input variables are added to the data frame for convenience.The arguments are:
input_df - The history of the input variables.init_state - The initial state of the state variables.f_update - The state update function.The value of the run_simulation() function is a data frame with
columns for the input variables, state variables, and time (\(t\)). There
is one row for each of the time steps (\(t = 1 \ldots n_{steps}\)).
The following sections set up an example of using run_simulation(). This
is a drastically scaled down example in that the number of time steps
and VSA vector dimensions are greatly reduced so that the simulation
result can be viewed in its entirety.
Set the dimensionality of the VSA vectors and the number of time steps in the simulation.
v_dim <- 10 # vector dimension of state variables (in practice = 1e4)
n_step <- 5 # number of time steps in simulation (in practice = 500)Create a data frame to hold the input values. Normally these will be from a file exported from the multicopter simulation.
The input values are contained in a data frame.
Each of the input variables is a time series - one value per time step. The data frame contains as many input variables as you need.
For this example we are just generating random input data. The input data for this project are all numeric scalars, so it could have been stored in a matrix, but in general, the inputs might be mixed types or complex structures so we use a data frame for generality.
input_df <- tibble::tibble(
i_x = rnorm(n = n_step),
i_y = rnorm(n = n_step)
)
input_df# A tibble: 5 × 2
i_x i_y
<dbl> <dbl>
1 -0.437 -0.634
2 0.329 0.628
3 -0.447 -0.752
4 -0.183 0.0409
5 1.67 -2.64 The initial state consists of whatever state variables the state update function refers to as previous state.
The previous state is represented as a one-row data frame with one column for each of the required state variables. The VSA vector variables need to be stored in list columns.
I expect that we will generally use a function to construct the initial state.
# Function to make the initial state
mk_init_state <- function(
v_dim, # integer[1] - dimension of vector-valued state variables
seed = NULL # integer[1] - random generation seed
) # value - dataframe[1, ] - initial state of system
{
set.seed(seed)
# Construct initial state
# MUST contain all columns used as previous state by update_state()
# Any other state columns are optional
tibble::tibble_row(
# scalar valued state variables
s_x = 0, s_y = 0,
# vector valued state variables (each must be wrapped in list())
s_0 = sample(c(-1, 1), size = v_dim, replace = TRUE) %>% list(),
s_1 = sample(c(-1, 1), size = v_dim, replace = TRUE) %>% list()
)
}
# Make the initial state
init_state <- mk_init_state(v_dim, seed = 42)
init_state# A tibble: 1 × 4
s_x s_y s_0 s_1
<dbl> <dbl> <list> <list>
1 0 0 <dbl [10]> <dbl [10]>str(init_state)tibble [1 × 4] (S3: tbl_df/tbl/data.frame)
$ s_x: num 0
$ s_y: num 0
$ s_0:List of 1
..$ : num [1:10] -1 -1 -1 -1 1 1 1 1 -1 1
$ s_1:List of 1
..$ : num [1:10] -1 1 -1 1 -1 -1 1 1 1 1The state update function takes the previous state and current input variables as arguments and returns the current state.
This specific update function is a gibberish example, but is generically the sort of thing I will be doing
The previous state is given as a one-row data frame. The VSA vector values must be stored as list columns.
The current input variables are given as a one-row data frame. For this project the input variables are numeric scalars which are represented as standard columns, but more generally the inputs may be more complex and require list columns.
The value returned by the state update function is a one-row data frame containing the updated values of all the state variables.
# Function to update state from previous state and current input
update_state <- function(
prev_state, # dataframe[1, ] - previous state
input # dataframe[1, ] - current input
)
{
# Update scalar valued state variables
s_x = prev_state$s_x + input$i_x
s_y = prev_state$s_y + input$i_y
# Update vector valued state variables
# List columns must be unlisted before use
s_0 = unlist(prev_state$s_0) * s_x
s_1 = unlist(prev_state$s_1) * s_y
s_2 = s_0 * s_1
s_3 = s_2 * s_0
s_4 = s_2 * s_1
s_5 = s_3 + s_4
# Construct and return a 1-row dataframe containing the updated state
tibble::tibble_row(
# Scalar valued state variables
s_x, s_y,
# Vector valued state variables
# List columns must be wrapped by list()
s_0 = list(s_0),
s_1 = list(s_1),
s_2 = list(s_2),
s_3 = list(s_3),
s_4 = list(s_4),
s_5 = list(s_5)
)
}Run the simulation based on the previous settings.
# Run the simulation, returning the history as a data frame
history_df <- input_df %>% run_simulation(init_state, update_state)
# Take a look at the shape of the history
history_df# A tibble: 5 × 11
t i_x i_y s_x s_y s_0 s_1 s_2 s_3 s_4 s_5
<int> <dbl> <dbl> <dbl> <dbl> <list> <list> <lis> <lis> <lis> <lis>
1 1 -0.437 -0.634 -0.437 -0.634 <dbl [10]> <dbl … <dbl… <dbl… <dbl… <dbl…
2 2 0.329 0.628 -0.109 -0.00641 <dbl [10]> <dbl … <dbl… <dbl… <dbl… <dbl…
3 3 -0.447 -0.752 -0.555 -0.759 <dbl [10]> <dbl … <dbl… <dbl… <dbl… <dbl…
4 4 -0.183 0.0409 -0.738 -0.718 <dbl [10]> <dbl … <dbl… <dbl… <dbl… <dbl…
5 5 1.67 -2.64 0.933 -3.36 <dbl [10]> <dbl … <dbl… <dbl… <dbl… <dbl…str(history_df)tibble [5 × 11] (S3: tbl_df/tbl/data.frame)
$ t : int [1:5] 1 2 3 4 5
$ i_x: num [1:5] -0.437 0.329 -0.447 -0.183 1.672
$ i_y: num [1:5] -0.6343 0.6279 -0.7524 0.0409 -2.6394
$ s_x: num [1:5] -0.437 -0.109 -0.555 -0.738 0.933
$ s_y: num [1:5] -0.63429 -0.00641 -0.75879 -0.71792 -3.35736
$ s_0:List of 5
..$ : num [1:10] 0.437 0.437 0.437 0.437 -0.437 ...
..$ : num [1:10] -0.0475 -0.0475 -0.0475 -0.0475 0.0475 ...
..$ : num [1:10] 0.0264 0.0264 0.0264 0.0264 -0.0264 ...
..$ : num [1:10] -0.0195 -0.0195 -0.0195 -0.0195 0.0195 ...
..$ : num [1:10] -0.0182 -0.0182 -0.0182 -0.0182 0.0182 ...
$ s_1:List of 5
..$ : num [1:10] 0.634 -0.634 0.634 -0.634 0.634 ...
..$ : num [1:10] -0.00407 0.00407 -0.00407 0.00407 -0.00407 ...
..$ : num [1:10] 0.00309 -0.00309 0.00309 -0.00309 0.00309 ...
..$ : num [1:10] -0.00222 0.00222 -0.00222 0.00222 -0.00222 ...
..$ : num [1:10] 0.00744 -0.00744 0.00744 -0.00744 0.00744 ...
$ s_2:List of 5
..$ : num [1:10] 0.277 -0.277 0.277 -0.277 -0.277 ...
..$ : num [1:10] 0.000193 -0.000193 0.000193 -0.000193 -0.000193 ...
..$ : num [1:10] 8.14e-05 -8.14e-05 8.14e-05 -8.14e-05 -8.14e-05 ...
..$ : num [1:10] 4.31e-05 -4.31e-05 4.31e-05 -4.31e-05 -4.31e-05 ...
..$ : num [1:10] -0.000135 0.000135 -0.000135 0.000135 0.000135 ...
$ s_3:List of 5
..$ : num [1:10] 0.121 -0.121 0.121 -0.121 0.121 ...
..$ : num [1:10] -9.17e-06 9.17e-06 -9.17e-06 9.17e-06 -9.17e-06 ...
..$ : num [1:10] 2.15e-06 -2.15e-06 2.15e-06 -2.15e-06 2.15e-06 ...
..$ : num [1:10] -8.4e-07 8.4e-07 -8.4e-07 8.4e-07 -8.4e-07 ...
..$ : num [1:10] 2.46e-06 -2.46e-06 2.46e-06 -2.46e-06 2.46e-06 ...
$ s_4:List of 5
..$ : num [1:10] 0.176 0.176 0.176 0.176 -0.176 ...
..$ : num [1:10] -7.86e-07 -7.86e-07 -7.86e-07 -7.86e-07 7.86e-07 ...
..$ : num [1:10] 2.51e-07 2.51e-07 2.51e-07 2.51e-07 -2.51e-07 ...
..$ : num [1:10] -9.56e-08 -9.56e-08 -9.56e-08 -9.56e-08 9.56e-08 ...
..$ : num [1:10] -1.01e-06 -1.01e-06 -1.01e-06 -1.01e-06 1.01e-06 ...
$ s_5:List of 5
..$ : num [1:10] 0.2972 0.0547 0.2972 0.0547 -0.0547 ...
..$ : num [1:10] -9.96e-06 8.38e-06 -9.96e-06 8.38e-06 -8.38e-06 ...
..$ : num [1:10] 2.40e-06 -1.89e-06 2.40e-06 -1.89e-06 1.89e-06 ...
..$ : num [1:10] -9.35e-07 7.44e-07 -9.35e-07 7.44e-07 -7.44e-07 ...
..$ : num [1:10] 1.45e-06 -3.46e-06 1.45e-06 -3.46e-06 3.46e-06 ...Increase the parameters to realistic values and run the simulation.
# Set global parameters
v_dim <- 1e4 # vector dimension of state variables
n_step <- 1e3 # number of time steps in simulation
# Generate input variables (random)
input_df <- tibble::tibble(
i_x = rnorm(n = n_step),
i_y = rnorm(n = n_step)
)
# Make the initial state
init_state <- mk_init_state(v_dim, seed = 42)
# Run the simulation, returning the history as a data frame
# Time the execution with tictoc::
tictoc::tic()
history_df <- input_df %>% run_simulation(init_state, update_state)
tictoc::toc()5.296 sec elapsed# Take a look at the history
history_df# A tibble: 1,000 × 11
t i_x i_y s_x s_y s_0 s_1 s_2 s_3 s_4 s_5
<int> <dbl> <dbl> <dbl> <dbl> <list> <list> <list> <list> <list> <list>
1 1 1.30 -0.298 1.30 -0.298 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
2 2 2.29 -0.284 3.59 -0.582 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
3 3 -1.39 0.870 2.20 0.287 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
4 4 -0.279 -0.544 1.92 -0.257 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
5 5 -0.133 0.629 1.79 0.372 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
6 6 0.636 -1.42 2.43 -1.05 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
7 7 -0.284 -1.23 2.14 -2.28 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
8 8 -2.66 -1.67 -0.514 -3.95 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
9 9 -2.44 0.0844 -2.95 -3.87 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
10 10 1.32 -0.206 -1.63 -4.07 <dbl [… <dbl … <dbl … <dbl … <dbl … <dbl …
# … with 990 more rows# How much RAM does the history use?
format(object.size(history_df), standard = "IEC", units = "GiB")[1] "0.4 GiB"That’s adequately fast.
The size is as expected.
sessionInfo()R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 21.04
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
locale:
[1] LC_CTYPE=en_AU.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_AU.UTF-8 LC_COLLATE=en_AU.UTF-8
[5] LC_MONETARY=en_AU.UTF-8 LC_MESSAGES=en_AU.UTF-8
[7] LC_PAPER=en_AU.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices datasets utils methods base
other attached packages:
[1] Matrix_1.3-4 DiagrammeR_1.0.6.1 tictoc_1.0.1 ggplot2_3.3.5
[5] dplyr_1.0.7 purrr_0.3.4 tibble_3.1.3
loaded via a namespace (and not attached):
[1] Rcpp_1.0.7 RColorBrewer_1.1-2 pillar_1.6.2 compiler_4.1.0
[5] later_1.2.0 git2r_0.28.0 workflowr_1.6.2 tools_4.1.0
[9] digest_0.6.27 lattice_0.20-44 jsonlite_1.7.2 evaluate_0.14
[13] lifecycle_1.0.0 gtable_0.3.0 pkgconfig_2.0.3 rlang_0.4.11
[17] rstudioapi_0.13 cli_3.0.1 yaml_2.2.1 xfun_0.24
[21] withr_2.4.2 stringr_1.4.0 knitr_1.33 htmlwidgets_1.5.3
[25] generics_0.1.0 fs_1.5.0 vctrs_0.3.8 rprojroot_2.0.2
[29] grid_4.1.0 tidyselect_1.1.1 here_1.0.1 glue_1.4.2
[33] R6_2.5.0 fansi_0.5.0 rmarkdown_2.9 bookdown_0.22
[37] magrittr_2.0.1 whisker_0.4 scales_1.1.1 promises_1.2.0.1
[41] ellipsis_0.3.2 htmltools_0.5.1.1 colorspace_2.0-2 renv_0.14.0
[45] httpuv_1.6.1 utf8_1.2.2 stringi_1.7.3 visNetwork_2.0.9
[49] munsell_0.5.0 crayon_1.4.1