vmax2

Vmax2 is a computational framework for planning motion trajectories that maximize a velocity-related objective under a set of kinematic and dynamic constraints. Seen as the successor to an earlier approach called Vmax, Vmax2 extends the problem to second-order dynamics and time-optimal considerations, making it suitable for systems with acceleration limits and actuator constraints. The typical goal is to produce a trajectory that achieves the highest feasible speed along a path while maintaining stability and safety.

The concept originated in control and robotics research in the 2010s, gaining traction as researchers sought methods capable of handling real-time constraints for autonomous platforms. Variants have been proposed to address discretization effects, model uncertainty, and multi-robot coordination, reflecting the need for robust performance across diverse operating conditions.

The problem is usually posed as a two-stage optimization: first establish feasibility given dynamics and bounds, then optimize the velocity objective. Many implementations rely on discretizing time or space and using convex relaxations or sequential quadratic programming. Some approaches exploit problem structure to reduce computational complexity, and in certain cases exact solutions are obtainable when dynamics are linear and costs are convex.

Applications of Vmax2-inspired planners span mobile robotics, robotic arms, drones, and automated warehouses. They are used to improve throughput, reduce travel time, and enhance energy efficiency while respecting safety and dynamic limits. The framework is often integrated with higher-level decision systems, perception modules, and control laws to form complete autonomous navigation pipelines.

Limitations include the need for accurate dynamic models and sensitivity to modeling errors. Computational demands can be high for high-dimensional systems, prompting ongoing research into real-time approximations, uncertainty handling, and tighter integration with perception and control.