Planning Piecewise Jerk Nonlinear Speed Optimizer Introduction

Introduction

This is an introduction of piecewise jerk nonlinear speed optimizer. For trajectory planning problems, the following three aspects need to be considered: 1)Task accomplishment. 2)Safety. 3)Comfort.
After a smooth driving guide line is generated, the trajectory is under the constraints of velocity bounds, acceleration bounds, jerk bounds, etc. Here, we formulate this problem as a quadratic programming problem.

Where is the code

Please refer code

Code Reading

PiecewiseJerkSpeedNonlinearOptimizer is a derived class whose base class is SpeedOptimizer. Thus, when task::Execute() is called in the task list, the Process() in PiecewiseJerkSpeedNonlinearOptimizer is actually doing the processing.

1. Input.
   The input includes PathData and initial TrajectoryPoint.
2. Process.

• Snaity Check. This ensures speed_data is not null and Speed Optimizer does not receive empty path data.
• const auto problem_setups_status = SetUpStatesAndBounds(path_data, *speed_data); The qp problem is initialized here. The next code line will clear speed_data if it fails.
• const auto qp_smooth_status = OptimizeByQP(speed_data, &distance, &velocity, &acceleration); It sloves the QP problem and the distance/velocity/acceleration are achieved. Still, speed_data is cleared if it fails.
• const bool speed_limit_check_status = CheckSpeedLimitFeasibility(); It checks first point of speed limit. Then the following four steps are processed: 1)Smooth Path Curvature 2)SmoothSpeedLimit 3)Optimize By NLP 4)Record speed_constraint
• Add s/t/v/a/jerk into speed_data and add enough zeros to avoid fallback

3. Output.
   The output is SpeedData, which includes s/t/v/a/jerk of the trajectory.

Algorithm Detail

Paper Reference:

• Optimal Trajectory Generation for Autonomous Vehicles UnderCentripetal Acceleration Constraints for In-lane Driving Scenarios
• DL-IAPS and PJSO: A Path/Speed Decoupled Trajectory Optimization and its Application in Autonomous Driving