ODtraject

ODtraject is a computational framework for computing optimal trajectories of dynamical systems under constraints. It combines elements of trajectory optimization and real-time planning to produce feasible control sequences that minimize a chosen cost function while respecting dynamics, actuator limits, safety constraints, and obstacle avoidance.

The core idea is to represent trajectories with time-indexed variables, typically using splines or piecewise polynomials, and to formulate a constrained optimization problem. The objective can include travel time, energy consumption, precision, and risk terms. Dynamics are enforced by a discrete-time model or a linearized approximation. Constraints cover state and input bounds, collision avoidance via soft or hard constraints, and environmental constraints. Solutions are often obtained by model predictive control (MPC) or direct transcription with gradient-based solvers; some implementations blend sampling-based planning with optimization to handle nonconvexities.

ODtraject is used in robotics, autonomous vehicles, drone flight, and industrial automation. It is also adopted in computer graphics for animation of character motion and in simulation-based training. Variants emphasize different aspects, such as robustness to disturbances, stochastic constraints, or real-time re-planning.

Limitations include computational demand, especially for high-dimensional systems or tight time horizons; sensitivity to model errors; the need for accurate obstacle representations; and challenges ensuring global optimality in nonconvex problems. Research tends to focus on improving scalability, real-time performance, and integration with perception systems.

See also: trajectory optimization, model predictive control, motion planning, nonlinear optimization.