PID Longitudinal Controller

Purpose / Use cases

The longitudinal_controller computes the target acceleration to achieve the target velocity set at each point of the target trajectory using a feed-forward/back control.

It also contains a slope force correction that takes into account road slope information, and a delay compensation function. It is assumed that the target acceleration calculated here will be properly realized by the vehicle interface.

Note that the use of this module is not mandatory for Autoware if the vehicle supports the "target speed" interface.

Design / Inner-workings / Algorithms

States

This module has four state transitions as shown below in order to handle special processing in a specific situation.

• DRIVE
  • Executes target velocity tracking by PID control.
  • It also applies the delay compensation and slope compensation.
• STOPPING
  • Controls the motion just before stopping.
  • Special sequence is performed to achieve accurate and smooth stopping.
• STOPPED
  • Performs operations in the stopped state (e.g. brake hold)
• EMERGENCY.
  • Enters an emergency state when certain conditions are met (e.g., when the vehicle has crossed a certain distance of a stop line).
  • The recovery condition (whether or not to keep emergency state until the vehicle completely stops) or the deceleration in the emergency state are defined by parameters.

The state transition diagram is shown below.

Logics

Control Block Diagram

FeedForward (FF)

The reference acceleration set in the trajectory and slope compensation terms are output as a feedforward. Under ideal conditions with no modeling error, this FF term alone should be sufficient for velocity tracking.

Tracking errors causing modeling or discretization errors are removed by the feedback control (now using PID).

Brake keeping

From the viewpoint of ride comfort, stopping with 0 acceleration is important because it reduces the impact of braking. However, if the target acceleration when stopping is 0, the vehicle may cross over the stop line or accelerate a little in front of the stop line due to vehicle model error or gradient estimation error.

For reliable stopping, the target acceleration calculated by the FeedForward system is limited to a negative acceleration when stopping.

Slope compensation

Based on the slope information, a compensation term is added to the target acceleration.

There are two sources of the slope information, which can be switched by a parameter.

• Pitch of the estimated ego-pose (default)
  • Calculates the current slope from the pitch angle of the estimated ego-pose
  • Pros: Easily available
  • Cons: Cannot extract accurate slope information due to the influence of vehicle vibration.
• Z coordinate on the trajectory
  • Calculates the road slope from the difference of z-coordinates between the front and rear wheel positions in the target trajectory
  • Pros: More accurate than pitch information, if the z-coordinates of the route are properly maintained
  • Pros: Can be used in combination with delay compensation (not yet implemented)
  • Cons: z-coordinates of high-precision map is needed.
  • Cons: Does not support free space planning (for now)

We also offer the options to switch between these, depending on driving conditions.

Notation: This function works correctly only in a vehicle system that does not have acceleration feedback in the low-level control system.

This compensation adds gravity correction to the target acceleration, resulting in an output value that is no longer equal to the target acceleration that the autonomous driving system desires. Therefore, it conflicts with the role of the acceleration feedback in the low-level controller. For instance, if the vehicle is attempting to start with an acceleration of 1.0 m/s^2 and a gravity correction of -1.0 m/s^2 is applied, the output value will be 0. If this output value is mistakenly treated as the target acceleration, the vehicle will not start.

A suitable example of a vehicle system for the slope compensation function is one in which the output acceleration from the longitudinal_controller is converted into target accel/brake pedal input without any feedbacks. In this case, the output acceleration is just used as a feedforward term to calculate the target pedal, and hence the issue mentioned above does not arise.

Note: The angle of the slope is defined as positive for an uphill slope, while the pitch angle of the ego pose is defined as negative when facing upward. They have an opposite definition.

PID control

For deviations that cannot be handled by FeedForward control, such as model errors, PID control is used to construct a feedback system.

This PID control calculates the target acceleration from the deviation between the current ego-velocity and the target velocity.

This PID logic has a maximum value for the output of each term. This is to prevent the following:

• Large integral terms may cause unintended behavior by users.
• Unintended noise may cause the output of the derivative term to be very large.

Note: by default, the integral term in the control system is not accumulated when the vehicle is stationary. This precautionary measure aims to prevent unintended accumulation of the integral term in scenarios where Autoware assumes the vehicle is engaged, but an external system has immobilized the vehicle to initiate startup procedures.

However, certain situations may arise, such as when the vehicle encounters a depression in the road surface during startup or if the slope compensation is inaccurately estimated (lower than necessary), leading to a failure to initiate motion. To address these scenarios, it is possible to activate error integration even when the vehicle is at rest by setting the enable_integration_at_low_speed parameter to true.

When enable_integration_at_low_speed is set to true, the PID controller will initiate integration of the acceleration error after a specified duration defined by the time_threshold_before_pid_integration parameter has elapsed without the vehicle surpassing a minimum velocity set by the current_vel_threshold_pid_integration parameter.

The presence of the time_threshold_before_pid_integration parameter is important for practical PID tuning. Integrating the error when the vehicle is stationary or at low speed can complicate PID tuning. This parameter effectively introduces a delay before the integral part becomes active, preventing it from kicking in immediately. This delay allows for more controlled and effective tuning of the PID controller.

At present, PID control is implemented from the viewpoint of trade-off between development/maintenance cost and performance. This may be replaced by a higher performance controller (adaptive control or robust control) in future development.

Time delay compensation

At high speeds, the delay of actuator systems such as gas pedals and brakes has a significant impact on driving accuracy. Depending on the actuating principle of the vehicle, the mechanism that physically controls the gas pedal and brake typically has a delay of about a hundred millisecond.

In this controller, the predicted ego-velocity and the target velocity after the delay time are calculated and used for the feedback to address the time delay problem.

Slope compensation

Based on the slope information, a compensation term is added to the target acceleration.

There are two sources of the slope information, which can be switched by a parameter.

• Pitch of the estimated ego-pose (default)
  • Calculates the current slope from the pitch angle of the estimated ego-pose
  • Pros: Easily available
  • Cons: Cannot extract accurate slope information due to the influence of vehicle vibration.
• Z coordinate on the trajectory
  • Calculates the road slope from the difference of z-coordinates between the front and rear wheel positions in the target trajectory
  • Pros: More accurate than pitch information, if the z-coordinates of the route are properly maintained
  • Pros: Can be used in combination with delay compensation (not yet implemented)
  • Cons: z-coordinates of high-precision map is needed.
  • Cons: Does not support free space planning (for now)

Assumptions / Known limits

1. Smoothed target velocity and its acceleration shall be set in the trajectory
   1. The velocity command is not smoothed inside the controller (only noise may be removed).
   2. For step-like target signal, tracking is performed as fast as possible.
2. The vehicle velocity must be an appropriate value
   1. The ego-velocity must be a signed-value corresponding to the forward/backward direction
   2. The ego-velocity should be given with appropriate noise processing.
   3. If there is a large amount of noise in the ego-velocity, the tracking performance will be significantly reduced.
3. The output of this controller must be achieved by later modules (e.g. vehicle interface).
   1. If the vehicle interface does not have the target velocity or acceleration interface (e.g., the vehicle only has a gas pedal and brake interface), an appropriate conversion must be done after this controller.

Inputs / Outputs / API

Input

Set the following from the controller_node

• autoware_planning_msgs/Trajectory : reference trajectory to follow.
• nav_msgs/Odometry: current odometry

Output

Return LongitudinalOutput which contains the following to the controller node

• autoware_control_msgs/Longitudinal: command to control the longitudinal motion of the vehicle. It contains the target velocity and target acceleration.
• LongitudinalSyncData
  • velocity convergence(currently not used)

PIDController class

The PIDController class is straightforward to use. First, gains and limits must be set (using setGains() and setLimits()) for the proportional (P), integral (I), and derivative (D) components. Then, the velocity can be calculated by providing the current error and time step duration to the calculate() function.

Parameter description

The default parameters defined in param/lateral_controller_defaults.param.yaml are adjusted to the AutonomouStuff Lexus RX 450h for under 40 km/h driving.

Name	Type	Description	Default value
delay_compensation_time	double	delay for longitudinal control [s]	0.17
enable_smooth_stop	bool	flag to enable transition to STOPPING	true
enable_overshoot_emergency	bool	flag to enable transition to EMERGENCY when the ego is over the stop line with a certain distance. See emergency_state_overshoot_stop_dist.	true
enable_large_tracking_error_emergency	bool	flag to enable transition to EMERGENCY when the closest trajectory point search is failed due to a large deviation between trajectory and ego pose.	true
enable_slope_compensation	bool	flag to modify output acceleration for slope compensation. The source of the slope angle can be selected from ego-pose or trajectory angle. See use_trajectory_for_pitch_calculation.	true
enable_brake_keeping_before_stop	bool	flag to keep a certain acceleration during DRIVE state before the ego stops. See Brake keeping.	false
enable_keep_stopped_until_steer_convergence	bool	flag to keep stopped condition until until the steer converges.	true
max_acc	double	max value of output acceleration [m/s^2]	3.0
min_acc	double	min value of output acceleration [m/s^2]	-5.0
max_jerk	double	max value of jerk of output acceleration [m/s^3]	2.0
min_jerk	double	min value of jerk of output acceleration [m/s^3]	-5.0
use_trajectory_for_pitch_calculation	bool	If true, the slope is estimated from trajectory z-level. Otherwise the pitch angle of the ego pose is used.	false
lpf_pitch_gain	double	gain of low-pass filter for pitch estimation	0.95
max_pitch_rad	double	max value of estimated pitch [rad]	0.1
min_pitch_rad	double	min value of estimated pitch [rad]	-0.1

State transition

Name	Type	Description	Default value
drive_state_stop_dist	double	The state will transit to DRIVE when the distance to the stop point is longer than drive_state_stop_dist + drive_state_offset_stop_dist [m]	0.5
drive_state_offset_stop_dist	double	The state will transit to DRIVE when the distance to the stop point is longer than drive_state_stop_dist + drive_state_offset_stop_dist [m]	1.0
stopping_state_stop_dist	double	The state will transit to STOPPING when the distance to the stop point is shorter than stopping_state_stop_dist [m]	0.5
stopped_state_entry_vel	double	threshold of the ego velocity in transition to the STOPPED state [m/s]	0.01
stopped_state_entry_acc	double	threshold of the ego acceleration in transition to the STOPPED state [m/s^2]	0.1
emergency_state_overshoot_stop_dist	double	If enable_overshoot_emergency is true and the ego is emergency_state_overshoot_stop_dist-meter ahead of the stop point, the state will transit to EMERGENCY. [m]	1.5
emergency_state_traj_trans_dev	double	If the ego's position is emergency_state_traj_tran_dev meter away from the nearest trajectory point, the state will transit to EMERGENCY. [m]	3.0
emergency_state_traj_rot_dev	double	If the ego's orientation is emergency_state_traj_rot_dev rad away from the nearest trajectory point orientation, the state will transit to EMERGENCY. [rad]	0.784

DRIVE Parameter

Name	Type	Description	Default value
kp	double	p gain for longitudinal control	1.0
ki	double	i gain for longitudinal control	0.1
kd	double	d gain for longitudinal control	0.0
max_out	double	max value of PID's output acceleration during DRIVE state [m/s^2]	1.0
min_out	double	min value of PID's output acceleration during DRIVE state [m/s^2]	-1.0
max_p_effort	double	max value of acceleration with p gain	1.0
min_p_effort	double	min value of acceleration with p gain	-1.0
max_i_effort	double	max value of acceleration with i gain	0.3
min_i_effort	double	min value of acceleration with i gain	-0.3
max_d_effort	double	max value of acceleration with d gain	0.0
min_d_effort	double	min value of acceleration with d gain	0.0
lpf_vel_error_gain	double	gain of low-pass filter for velocity error	0.9
enable_integration_at_low_speed	bool	Whether to enable integration of acceleration errors when the vehicle speed is lower than current_vel_threshold_pid_integration or not.	false
current_vel_threshold_pid_integration	double	Velocity error is integrated for I-term only when the absolute value of current velocity is larger than this parameter. [m/s]	0.5
time_threshold_before_pid_integration	double	How much time without the vehicle moving must past to enable PID error integration. [s]	5.0
brake_keeping_acc	double	If enable_brake_keeping_before_stop is true, a certain acceleration is kept during DRIVE state before the ego stops [m/s^2] See Brake keeping.	0.2

STOPPING Parameter (smooth stop)

Smooth stop is enabled if enable_smooth_stop is true. In smooth stop, strong acceleration (strong_acc) will be output first to decrease the ego velocity. Then weak acceleration (weak_acc) will be output to stop smoothly by decreasing the ego jerk. If the ego does not stop in a certain time or some-meter over the stop point, weak acceleration to stop right (weak_stop_acc) now will be output. If the ego is still running, strong acceleration (strong_stop_acc) to stop right now will be output.

Name	Type	Description	Default value
smooth_stop_max_strong_acc	double	max strong acceleration [m/s^2]	-0.5
smooth_stop_min_strong_acc	double	min strong acceleration [m/s^2]	-0.8
smooth_stop_weak_acc	double	weak acceleration [m/s^2]	-0.3
smooth_stop_weak_stop_acc	double	weak acceleration to stop right now [m/s^2]	-0.8
smooth_stop_strong_stop_acc	double	strong acceleration to be output when the ego is smooth_stop_strong_stop_dist-meter over the stop point. [m/s^2]	-3.4
smooth_stop_max_fast_vel	double	max fast vel to judge the ego is running fast [m/s]. If the ego is running fast, strong acceleration will be output.	0.5
smooth_stop_min_running_vel	double	min ego velocity to judge if the ego is running or not [m/s]	0.01
smooth_stop_min_running_acc	double	min ego acceleration to judge if the ego is running or not [m/s^2]	0.01
smooth_stop_weak_stop_time	double	max time to output weak acceleration [s]. After this, strong acceleration will be output.	0.8
smooth_stop_weak_stop_dist	double	Weak acceleration will be output when the ego is smooth_stop_weak_stop_dist-meter before the stop point. [m]	-0.3
smooth_stop_strong_stop_dist	double	Strong acceleration will be output when the ego is smooth_stop_strong_stop_dist-meter over the stop point. [m]	-0.5

STOPPED Parameter

The STOPPED state assumes that the vehicle is completely stopped with the brakes fully applied. Therefore, stopped_acc should be set to a value that allows the vehicle to apply the strongest possible brake. If stopped_acc is not sufficiently low, there is a possibility of sliding down on steep slopes.

Name	Type	Description	Default value
stopped_vel	double	target velocity in STOPPED state [m/s]	0.0
stopped_acc	double	target acceleration in STOPPED state [m/s^2]	-3.4
stopped_jerk	double	target jerk in STOPPED state [m/s^3]	-5.0

EMERGENCY Parameter

Name	Type	Description	Default value
emergency_vel	double	target velocity in EMERGENCY state [m/s]	0.0
emergency_acc	double	target acceleration in an EMERGENCY state [m/s^2]	-5.0
emergency_jerk	double	target jerk in an EMERGENCY state [m/s^3]	-3.0

References / External links

Future extensions / Unimplemented parts

Related issues