Dynamic Motion Planning with Project Varuna

Curvature-Based Reachability Planner

The Curvature-based Reachability Planner, as seen in the first figure, utilizes a family of switched Koopman models (MMPK) to sample a set of feasible trajectories ahead in time.

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For each of the models, a control input is identified to satisfy the curvature constraints, and an open-loop prediction enables the sampling of multiple trajectories.

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The trajectory and curvature mode that aligns the most with the global reference path is selected, allowing for course correction in presence of unmodeled dynamics.

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This planner is best suited for on-road applications with unmodeled dynamics from either mechanical wear on the robot or slight variations in terrain profile / surface friction, which manifest as Sim2Real gap compromising tracking capabilities. 

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More details on the mechanics of the planner and detailed analysis on simulation/hardware tests can be found in our paper here​.

Load-Transfer Based Reachability Planner

The Load-Transfer Based Reachability Planner offers an advanced solution for off-road environments using Adaptive MMPK models. By sampling trajectories that account for both curvature requirements and real-time load transfers, this planner ensures precise path tracking in even the most challenging terrains.

The control inputs are modulated based on the vehicle’s real-time center of gravity (CG) position, enabling responsive open-loop predictions. As depicted in the figures, the resulting trajectories adapt dynamically to terrain-induced load transfers, providing a robust and efficient approach to off-road path-planning.

Combined with Adaptive MMPK workflow, this planner is instrumental in pushing the boundaries of off-road path tracking and delivering highly adaptive solutions for demanding and unpredictable environments.