Minimum Time

Minimum-time trajectory generation focuses on finding the fastest path for a system to move between specified points, often subject to constraints like velocity, acceleration, or actuator limitations. Current research explores this problem across diverse applications, employing techniques such as differential game theory, numerical optimization (including nonlinear programming and alternating optimization methods), and graph-based approaches like trajectory retiming, often adapting these to specific system models (e.g., Dubins cars, quadrotors, UAV fleets). These advancements have significant implications for robotics, autonomous systems, and machine learning, enabling more efficient motion planning and improved performance in tasks ranging from surveillance to disaster response and federated learning.