A near-minimum time feedback controller for robotic manipulators with bounded input torques is developed. Since the bang-bang input torque obtained from the timeoptimal control theory leaves little or no room for the extra torque of the feedback control action, it is difficult to combine a minimum time open-loop controller with an additional feedback controller. A simple solution to this problem has been to solve the minimum time problem using arbitrarily reduced torque bounds so that a torque head room is created for the feedback control action. Such a scheme, however, wastes considerable input torque potential and gives significantly larger execution time of the trajectory than the theoretical minimum time calculated from the time-optimal control theory. A stable feedback controller is developed in this paper which applies a time scaling method to move a manipulator in near-minimum time using the allowable input torques efficiently. This new feedback controller algorithm adapts to an uncertain environment and automatically adjusts the desired speed along a specified path to be as fast as possible while avoiding the velocity saturation condition. Numerical examples of the near-minimum time feedback controller are provided using a two-link SCARA manipulator.
Study of kinematics and dynamics of machinery involves very challenging mathematics for engineering technology students who typically take this course at their junior level in a 4-year baccalaureate curriculum. Although mathematics is an essential tool for designing and analyzing mechanisms, this heavy burden in mathematics carries a risk of taking students' attention away from developing the important fundamental concepts of kinematics which are truly beneficial in their future practical technical work. This paper describes an attempt at WSU to develop an experimental kinematics and dynamics course such that students learn the subject from concept and experience. In this method, students are first challenged to solve kinematics problems through the computer simulation software Working Model without knowing the underlying mathematical tools. In this challenge, students will improve the simulation results through trial and error and their own approaches. In most cases, they will realize that the perfect solution has to be obtained from an approach they do not yet know. This challenge will provide them with the experience to develop a concept of each kinematics problem. Only after this challenge, will students be exposed to mathematical approaches to provide perfect solutions to challenge the problems. Finally, they will try another set of simulations using the mathematical approaches they mastered and verify the validity of the mathematical approaches. I.
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