Optimal trajectory planning for robotic manipulators in the presence of obstacles
Yao‐Chon Chen · 1988
In this thesis, the optimal trajectory planning problem for robotic manipulators in the presence of obstacles is treated as an optimal control problem with state space constraints, described by a set of functional inequalities in the generalized coordinates of the robotic manipulator. A new approach for modeling the obstacles is proposed. The main idea of the proposed approach is to model an obstacle as a composition of primitive objects in the joint space of the robotic manipulator. The discussion is centered on stationary obstacles, but it is also shown that time-varying obstacles can be handled easily if their motions are deterministic. Using the proposed approach, closed-form approximations for obstacles in the joint space are determined by solving a finite-dimensional constrained optimization problem. These closed-form expressions are then used to formulate the optimal trajectory planning problem as an optimal control problem with state space constraints. A recently proposed numerical algorithm is then used to solve the resulting optimal control problem. Solutions to several example problems using the minimum-time and minimum-energy optimality criteria are presented. It is also shown in this thesis that the optimal trajectory tracking problem for robotic manipulators in the presence of obstacles can be formulated as an optimal control problem with state space constraints. In this case the constraints are described by a set of functional equality and inequality constraints on the generalized coordinates of the manipulator. A new definition of the tracking error is developed and is applied to the formulation.