Trajectory optimisation is the computation of a path and control profile for a dynamic system that minimises a cost subject to physical and operational constraints. It is widely used in robotics, aerospace and autonomous vehicles.
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- Trajectory optimisation formulates motion as an optimal control problem, seeking state and input sequences that minimise a cost such as time, energy or jerk while satisfying dynamics, actuator limits and obstacle constraints. Solution methods include direct collocation, shooting methods and differential dynamic programming.
- In robotics it produces smooth, dynamically feasible motions for manipulators and mobile platforms, often refining coarse paths from a planner. The approach connects motion planning with control theory by jointly reasoning about geometry and system dynamics.