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