A novel variational approach for collision-free trajectory planning of robot manipulators

The objective of the paper is to establish a mathematical framework for the variational approach for collision free trajectory planning of a robot manipulator, examine it from an engineering perspective and demonstrate the importance of the dynamic characteristics. The framework is based on the energetic concept of an instantaneous energy balance of a dynamic system. Within the framework, different energy forms are defined for obstacle, environmental constraints and task requirements according to their functional characteristics. By applying Hamilton's principle, the general differential control equations of the system are derived. The simulated results demonstrate the elegance and robustness of the current variational approach.