MMPK-Deployment-Results

This repository serves as a supplemental documentation of the test scenarios and results presented for our novel end-to-end data-driven (modeling/planning/control) framework called the Multi-Model Parameterized Koopman (MMPK) framework.

Abstract:

This research introduces the Multi-Model Parameterized Koopman (MMPK) framework, a novel data-driven approach for enabling autonomous navigation in autonomous ground vehicles. MMPK builds upon the Koopman Extended Dynamic Mode Decomposition (KEDMD) algorithm, offering a flexible modeling and control solution. Unlike traditional methods, MMPK addresses challenges such as overfitting and reliance on a single model by adopting a pose-agnostic representation of positional data and employing a set of parameterized models based on curvature. Additionally, the MMPK approach effectively mitigates data bias and reduces dependency on a singular global model. Our paper presents an end-to-end unified pipeline encompassing offline MMPK modeling and an online outer-loop control design consisting of model-based trajectory planning and linear Model Predictive Control adapted to switched Koopman dynamics. Comparative evaluations demonstrate MMPK's superior path-tracking capabilities and the effectiveness of its local planning strategy in bridging the model-sim-real gap.

Paper (Preprint):
Data-Driven Modeling and Experimental Validation of Autonomous Vehicles using Koopman Operator

Repository Organization

Figures: This folder contains all the plots from the experiment.
Videos: Folder for storing video results from MMPK hardware deployment.

MMPK Framework

The framework can be broken down into following process flows.

Data-gathering/Model-training (Offline):
- First, we collect data of a vehicle undergoing maneuvers resulting in roll/yaw plane excitation.
- The data is then converted into body-frame representation.
- Finally, it is split into distinct buckets based on the curvature bins.
Parameterized family of Koopman models (Offline):
- For each of the curvature bins, the associated set of state, control, and output matrix are approximated.
- Once trained, these models are directly used for the control loop.
Outer control loop (Online):
- For the online real-time deployment, the reference trajectory and the pose estimate of the vehicle are sent to the local motion planner.
- The local planner samples all the feasible trajectories across models and chooses the one closest to the reference trajectory.
- This reference trajectory along with the selected curvature is passed forward to the linear MPC.
- The linear MPC produces high-level commands (velocity steering) for the vehicle.

Experiment Setup

The following diagram presents pictorial representation for host of experimental stipulations for thorough validation of MMPK framework in simulation and hardware deployment settings.

The experiments are divided into two sections: Experiment I for deployment in the simulation environment and Experiment II for hardware deployment.
Experiment I-A to I-D:
In this setup, we are evaluating model v/s simulation disparity and effect of pose feedback and parameterized Koopman models and their effect on tracking performance across reference trajectories in the test dataset. Following are the stipulations for each of the test cases:

Experiment I-A: Single model with quintic sampling and model feedback from MPC as pose estimate.
Experiment I-B: Single model with quintic sampling and pose feedback from simulation as pose estimate.
Experiment I-C: Parameterized model with reachability based motion planning and model feedback from MPC as pose estimate.
Experiment I-D: Parameterized model with reachability based motion planning and feedback from simulation as pose estimate .

Experiment II-A to II-D:
In the following experiments , we evaluate the disparity between model and hardware and the impact of pose feedback and parameterized Koopman models on tracking performance across reference trajectories in the test dataset. The stipulations for each test case are as follows:

Experiment II-A and II-C: Similar to Experiments I-A and I-C, the feedback is agnostic to the actual realization of motion for the robot in simulation and on hardware.
Experiment II-B and II-D: Similar to Experiments I-B and I-D, the only difference is that the pose feedback is achieved from LiDAR- based odometry

we have considered 8 models as a baseline for MMPK It means that the entire operational range of the vehicle is broken down into 8 discrete bins. For each of the data points, curvature of instantaneous reference trajectory is captured through the motion planner and fit into one of the 8 bins of operation. Thus, all the box and whisker plots are split in these 8 bins even where the number of models and their associated curvature bins of operation vary but are approximated with 8 reference bins to maintain consistency in comparison as represented visually in the figure below.