Modeling of Vehicle Dynamics with Project Varuna

Highlighted below are multiple modeling choices embedded in the Project Varuna framework. These range from modeling for small-scale vehicles to mid-full scale vehicles deployed in on-road and off-road navigation scenarios.

Modeling for Small-Scale Vehicles

Using the Koopman Extended Dynamic Mode Decomposition (EDMD) technique, we can obtain a single model of the vehicle dynamics based on pose information and control inputs.

We follow a 4 step process:

Data collection with help of indoor localization system
Candidate function selection for Koopman lifting
(Deeper analysis presented in our IROS and MECC paper!)
A single Koopman model is identified with EDMD
Using the identified model, a linear MPC is used for path tracking realization

This approach works best for small-scale robots operating in indoor fixed spaces.

Multi-model Parameterized Koopman (MMPK) for On-road UGVs

The Multi-Model Parameterized Koopman (MMPK) framework blends traditional robotics modeling and motion planning with Koopman Operator Theory (KOT) to meet the unique demands of Uncrewed Ground Vehicles (UGVs). MMPK offers a global-frame independent dynamics formulation using a body-frame representation and adapts to changing conditions with curvature-parameterized Koopman models, enhancing fault tolerance and reducing data bias. MMPK has also enabled the creation of our novel reachability planners (highlighted on Motion Planning page), which generates and selects optimal trajectories in real-time, while the enhanced control loop with linear MPC improves trajectory tracking and mitigates the Sim2Real gap.

This approach is best suited to model on-road UGVs at all scales, even in the presence of unmodeled dynamics and slight variability in terrain properties.

Adaptive MMPK for Off-road UGVs

This technique introduces a novel approach for modeling the highly nonlinear effects of terrain perturbation and load transfers typically indicative of uneven offroad terrain.

We present a novel perspective on the representation of vehicle dynamics before applying the Koopman operator for global linearization. Regardless of the model’s fidelity and the number of states considered, the vehicle will always operate within and evolve on a SE2 manifold. By extending this principle to offroad dynamics, we can model the effect of varying terrain as disturbances on the SE2 manifold that manifest as an additional matrix that acts linearly in the lifted functional space. This is termed as the Adaptive MMPK approach.

In practical terms, this innovative method allows for more accurate, data-driven modeling of vehicle dynamics across a wide range of conditions, making it ideal for UGVs operating in harsh real-world off-road environments.