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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : European Journal of Mechanics - A/Solids, Volume 23, Issue 4, July–August 2004, Pages 703–715
We discuss the problem of minimum cost trajectory planning for robotic manipulators. It consists of linking two points in the operational space while minimizing a cost function, taking into account dynamic equations of motion as well as bounds on joint positions, velocities, jerks and torques. This generic optimal control problem is transformed, via a clamped cubic spline model of joint temporal evolutions, into a non-linear constrained optimization problem which is treated then by the Sequential Quadratic Programming (SQP) method. Applications involving grasping mobile object or obstacle avoidance are shown to illustrate the efficiency of the proposed planner.
Due to their great ability of speed and precision and their cost-effectiveness in repetitive tasks, industrial robots have been used for decade in place of human workers in automatic production lines. But these powerful machines are hardly autonomous in the sense that they require preliminary actions, such as calibration or motion planning, to achieve specified tasks. In general, robotic manipulators are used at their limit capacities for obvious reasons of productivity. This leads, however, to quite significant joint torque and velocity magnitudes which can be harmful to the system state. In order to increase the manipulator performances, it is highly desirable to control the system dynamic taking into account technological, geometrical and environmental constraints as well as any other constraints inherent both to the robot design and to the nature of the task to be executed. Since many different ways are possible to perform the same task, this freedom of choice can be exploited judiciously to optimize a given performance criterion.