Formulation and optimization of cubic polynomial joint trajectories for mechanical manipulators

Abstract

Because of physical constraints, the optimum control of industrial robots is a difficult problem. An alternative approach is to divide the problem into two parts: optimum pat,h planning for off-line processing followed by on-line path tracking. The path tracking can be achieved by adopting the existing approach. The path planning is done at the joint level. Cubic spline functions are used for constructing joint trajectories for mechanical manipulators. The motion of the manipulator is specified by a sequence of Cartesian knots, i.e. positions and orientations of the hand. For a &joint manipulator, these Cartesian knots are transformed into six sets of joint values, with each set corresponding to a joint. Piecewise cubic polynomials are used to fit the sequence of joint values for each of the six joints. The problem is proved to be uniquely solvable. Furthermore, an algorithm is developed to schedule the time periods between each pair of adjacent knots such that the total traveling time is minimized subject to the physical constraints on joint velocities, accelerations, and jerks. FORTRAh' programs have been written to implement (1) the procedure for constructing the cubic polynomial joint trajectories and (2) the algorithm for minimizing the traveling time. Results are given as an illustration.

Variational dynamic interpolation for kinematic systems on trivial principal bundles

“…Our work is inspired by the tracking problem for systems which are required to pass through certain ordered set of points on the configuration space. This is called as the dynamic interpolation problem and some of the early work on the topic is presented in [1], [2]. The idea of such interpolating curves on non-Euclidean spaces for applications to robotics first appears in [3].…”

Optimal trajectory planning for industrial robots using harmony search algorithm

“…Many optimization algorithms have been applied in trajectory optimization in the existing literatures, such as the flexible polyhedron search (FPS) algorithm (Wang and Horng, 1990;Lin et al, 1983), the interval analysis algorithm (Piazzi and Visioli, 2000), and the sequential quadratic programming (SQP) method (Chettibi et al, 2004;Gasparetto and Zanotto, 2010;Zanotto et al, 2011). These algorithms are non-heuristic and have some common drawbacks: the result may be a local optimum instead of a global optimum, they need a suitable initial solution (which could affect the execution time and even the final result of the optimization algorithm), etc.…”

Minimum time collision-free path planning for robotic assembly

“…The problems associated with path planning and optimization in robotic applications have been emphasized in the past (Kant and Zucker 1988, Lin et al 1983, Reif 1979, Wu 1989. Most of the reported solutions to these problems involve complex, nonlinear iterating procedures (Freund and Hoyer 1984, Kim and Shin 1985, Luh and Lin 1981, Trabia 1989.…”

“…The first one involves the determination of the shortest path ofthe manipulator's end effector from a pick position (feeders and magazines carrying individual components) to the place position (assembly fixtures), such that it avoids collisions with obstacles in the assembly area. The second objective is concerned with the determination of the levels of the robot control variables that will yield the minimum cycle time in order to increase productivity.The problems associated with path planning and optimization in robotic applications have been emphasized in the past (Kant and Zucker 1988, Lin et al 1983, Reif 1979, Wu 1989. Most of the reported solutions to these problems involve complex, nonlinear iterating procedures (Freund and Hoyer 1984, Kim and Shin 1985, Luh and Lin 1981, Trabia 1989.…”