Autonomous Driving
Perception
- Navigation tool
- Camera
- Radar
- LiDAR
- Infrared detector
- Speedometer
- veh-veh communication
- veh-infrastructure communication
Decision-making
- departure time
- good route
- good lane
- driving style
- way to accel/decel
- make a turn
- park location
Architecture
- Pre-trip
trip generation, modal choice, routine choice
- In-trip
Path planning, Maneuver regulation
- Post-trip
Parking
Pre-trip decisions
- Centralized
central command center send instructions
Some win, some lose
- Decentralized
plan trip independently, selfish
little communication
Sometime efficient, sometime inefficient
In-trip decisions
- offline info
static, in form of map
- online info
enable the route to be adapted to changing traffic conditions
Post-trip decision
Speed tracking
Dynamic system
- State Variable
$v[t]$
- State space
$R>= 0$
- Control input
$u[t]$(accel)
- System dynamic
$v[t+dt] = v[t]+u[t]*dt$
Open-loop control
Specify the control input $u[t]$ for all t in $[0,T]$
not a good idea for autonomous driving.
In practice, we need to consider the uncertainty of the system.
We should have:
$$
v[t+dt]=v[t]+u[t]dt+w(t)
$$
Where w(t) is the noise term capturing the uncertainty of the system.
Closed-loop control
Specify the control input $u[t]$ as a function of the state $v[t]$
able to adapt to the uncertainty of the system.
Compare the state $v[t]$ with the desired state $v_desired[t]$
Essentially, we need a mapping from state to control input
like map speed to acceleration
$$
v[t+dt]=v[t]+mu[v[t]]dt+w(t)
$$
Linear controller
the $u[t]$ has linear relationship with $v[t]$
$$
\mu[v] = k[v-v_{desired}]
$$
LTI system
linear time-invariant
Control of LTI system
exponential convergence is stronger than asymptotic convergent
if LTI system is asymptotic convergent, it is also exponential convergent
$$
x[t+1]=ax[t]+bu[t]
$$
Speed tracking
given:
$v_{desired}, \delta$
determine:
$u[t]$ $t = 0,1,2$
state
$v[t]$
$v[t+1] = v[t] + u[t]\delta + w[t]$
select $u[t]$ so that $w[t]$ will not accumulate
$u[t]=\mu(v[t]) = kv[t]$
$$
v[t+1] = f(v[t],u[t])
$$
Remember the review question
Trajectory tracking
Overview:
track means asymptotic convergent
$x[t]$ and $x_{desired}[t]$
$\lim_{t\rightarrow\infty}|x[t]-x_{desired}[t] | = 0$
state of system:$[x[t], v[t]]^T$
if successful:
$$
[x[t], v[t]]^T \rightarrow [x_{desired}[t], v_{desired}[t]]^T
$$
Control policy
- A control policy is a function
- This function maps a state to a control input
$$
u[t] = f(x[t],v[t])
$$
$$
u[t] = -k_1(x[t]-x_{desired}[t])-k_2(v[t]-v_{desired}[t])
$$
$$
k_1,k_2>0
$$
