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A new approach based on interval analysis is developed to find the global minimum-jerk (MJ) trajectory of a robot manipulator within a joint space scheme using cubic splines. MJ trajectories are desirable for their similarity to human joint movements and for their amenability to path tracking and to limit robot vibrations. This makes them attractive choices for robotic applications, in spite of the fact that the manipulator dynamics is not taken into account. Cubic splines are used in a framework that assures overall continuity of velocities and accelerations in the robot movement. The resulting MJ trajectory planning is shown to be a global constrained minimax optimization problem. This is solved by a newly devised algorithm based on interval analysis and proof of convergence with certainty to an arbitrarily good global solution is provided. The proposed planning method is applied to an example regarding a six-joint manipulator and comparisons with an alternative MJ planner are exposed.

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a b s t r a c tA new event-based proportional-integral controller, based on a specific send-on-delta sampling strategy, is analyzed in this paper. In particular, necessary and sufficient conditions on the controller parameters for the existence of equilibrium points without limit cycles are given for a first-order-plus-dead-time process. These conditions can be usefully exploited for the tuning of the controller, thus making the overall design easier. Practical issues related to the controller implementation are also addressed. Simulation and experimental results are provided as illustrative examples.

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In this paper, a novel methodology, based on fuzzy logic, for the tuning of proportional-integral-derivative (PID) controllers is presented. A fuzzy inference system is adopted to determine the value of the weight that multiplies the set-point for the proportional action, based on the current output error and its time derivative. In this way, both the overshoot and the rise time in set-point following can be reduced. The values of the proportional gain and the integral and derivative time constant are determined according to the well-known Ziegler-Nichols formula so that a good load disturbance attenuation is also assured. The methodology is shown to be effective for a large range of processes and is valuable to be adopted in industrial settings since it is intuitive, it requires only a small extra computational effort, and it is robust with regard to parameter variations. The tuning of the parameters of the fuzzy module can be easily done by hand or by means of an autotuning procedure based on genetic algorithms.