R/safecrossover.R

In cartools: Tools for Understanding Highway Performance

#' The function \code{safecrossover} a graph showing driver conflict of two vehicles changing lanes.
#'
#' @param umn average speed in mph, a number
#' @param leff effective vehicle length in feet, a number
#' @usage safecrossover(umn, leff)
#' @examples
#' safecrossover(67, 14)
#' @export
safecrossover <- function(umn, leff) {
  x <- y <- 0
  plot(x, y, type = "l", xlim = c(-20,20), ylim = c(-800,200), xlab = "",
       ylab = "", axes = FALSE)
  polygon(c(-12,-12,12,12,-12),c(-850,250,250,-850,-850),col = gray(0.9))
  abline(v = 0, col = gray(0.8))
  abline(h = c(0,-500), col = gray(0.8))
  lines(c(12,12), c(-850,250))
  lines(c(-12,-12), c(-850,250))
  lines(c(0,0), c(-850,250), lty = 2)
  axis(side = 1, at = 6, labels = "Lane 2", cex = 0.75)
  axis(side = 1, at = -6, labels = "Lane 1", cex = 0.75)
  axis(side = 2, at = -500, labels = "x = -500")
  axis(side = 2, at = 0, labels = "x = 0")
  text(6,-250, label = "Vehicle 2 yields", pos = 3)
  title(main = "Safe Crossover")
  axis(side = 1, at = 0, labels = "Upstream", line = 1, cex = 2)
  xstart <- -850
  xend   <- 250
  u0     <- umn * 5280/3600
  tend   <- (xend-xstart)/u0
  tseq   <- seq(0,tend,0.1)
  xseq   <- xab(xstart,u0,0,0,tseq,0)
  tlen   <- length(tseq)
  y      <- rep(NA, tlen)
  df     <- data.frame(t = tseq, x = xseq, y)
  for(i in 1: tlen) {
    if(df[i,2] >= 0) df[i,3] <- -6
    if(df[i,2] <= -500) df[i,3] <- 6
    if(-500 < df[i,2] & df[i,2] < 0) df[i,3] <- -12/500 * df[i,2] - 6
  }
  lines(-df[,3],df[,2], lwd = 3, col = "blue")
  points(0, max(df[df[,2] <= -250,2]), pch = 16)
  Vehicle <- rep(1, dim(df)[1])
  u       <- rep(u0, dim(df)[1])
  df <- cbind(df, Vehicle, u)
  # Vehicle 2 decelerate
  tstart <- max(df[df[,2] <= -500,1])
  ustart <- u0
  xstart <- max(df[df[,2] <= -500,2])
  tend   <- max(df[df[,2] <= -250,1])
  uend   <- u0
  xend   <- max(df[df[,2] <= -250,2]) - 2*leff
  ab     <- xabparam(tstart, tend, ustart, uend, xstart, xend)
  tseq2  <- seq(tstart,tend,0.1)
  tlen2  <- length(tseq2)
  u2     <- uab(u0, a = ab[1], b = ab[2], t = tseq2, t0 = tstart)
  x2     <- xab(x0 = xstart, u0, a = ab[1], b = ab[2], t = tseq2, t0 = tstart)
  df2a   <- data.frame(t = tseq2, u = u2, x = x2)
  # Vehicle 2 accelerate
  tstart <- tend
  ustart <- u0
  xstart <- xend
  tend   <- max(df[df[,2] <= 0,1])
  uend   <- u0
  xend   <- max(df[df[,2] <= 0,2])
  ab     <- xabparam(tstart, tend, ustart, uend, xstart, xend)
  tseq3  <- seq(tstart,tend,0.1)
  tlen3  <- length(tseq3)
  u3     <- uab(u0, a = ab[1], b = ab[2], t = tseq3, t0 = tstart)
  x3     <- xab(x0 = xstart, u0, a = ab[1], b = ab[2], t = tseq3, t0 = tstart)
  df2b   <- data.frame(t = tseq3, u = u3, x = x3)
  df2ab  <- rbind(df2a,df2b[-1,])
  df2    <- df
  points(0, df2a[dim(df2a)[1],3])
  tstart <- df2a[1,1]
  tend   <- df2b[dim(df2b)[1],1]
  df2[df2[,1] >= tstart & df2[,1] <= tend,2] <- df2ab[,3]
  lines(df2[,3],df2[,2], lwd = 3, col = "green")
  Vehicle <- rep(2, dim(df2)[1])
  tbegin  <- tseq[tseq < tstart]
  ubegin  <- rep(u0,length(tbegin))
  tup     <- tseq[tseq > tend]
  uup     <- rep(u0,length(tup))
  u       <- c(ubegin, df2ab[,2], uup)
  df2[,4] <- Vehicle
  df2[,5] <- u
  df      <- rbind(df,df2)
  df      <- df[df[,1] >= 3 & df[,1] <= 9,]
  return(df)
}