11. A computer software product, comprising a medium readable by a processor, the medium having stored thereon a set of instructions for planning the trajectory of a parallel kinematic machine, the set of instructions including: (a) a first sequence of instructions which, when executed by the processor, causes the processor to select new trajectory parameters from an offline dataset comprising a plurality of training trajectories; (b) a second sequence of instructions which, when executed by the processor, causes the processor to perform a trajectory initialization; (c) a third sequence of instructions which, when executed by the processor, causes the processor to formulate off-line, a mathematical description of a constrained optimization problem for trajectory planning of a parallel kinematic machine (PKM), the mathematical description including a cost minimization function and augmented Lagrange multipliers utilized in an augmented Lagrange decoupling procedure (ALD) to transform the problem into a non-constrained problem, an inertia matrix invertibility condition control law specification, a discrete dynamic model approximation using a multi-step Adams predictive-corrective formulation initialized with a fourth order Runge-Kutta, and a stopping criteria, wherein an iterative solution to the optimization problem describes at least one optimized trajectory; (d) a fourth sequence of instructions which, when executed by the processor, causes the processor to save the at least one optimized trajectory; (e) a fifth sequence of instructions which, when executed by the processor, causes the processor to initialize membership function parameters defining fuzzy sets and number of rules for a Tsukamoto neuro-fuzzy inference procedure; (f) a sixth sequence of instructions which, when executed by the processor, causes the processor to optimize the membership function parameters for inputs extracted from the at least one optimized trajectory and outputs of the Tsukamoto neuro-fuzzy inference procedure; (g) a seventh sequence of instructions which, when executed by the processor, causes the processor to perform on-line the Tsukamoto neuro-fuzzy inference procedure to further optimize the trajectory of the PKM, the on-line Tsukamoto neuro-fuzzy inference procedure accepting Cartesian 2-dimensional positions and velocities as fuzzy inputs, and outputting joint torques and sampling periods representing the further optimization of the at least one optimized trajectory; (h) a eighth sequence of instructions which, when executed by the processor, causes the processor to transfer to the parallel kinetic machine a resultant trajectory planning program based on the further optimization; whereby the PKM executes motion consistent with the further optimization of the at least one optimized trajectory so that time and energy of the PKM motion is optimally minimized.
11. A computer software product, comprising a medium readable by a processor, the medium having stored thereon a set of instructions for planning the trajectory of a parallel kinematic machine, the set of instructions including: (a) a first sequence of instructions which, when executed by the processor, causes the processor to select new trajectory parameters from an offline dataset comprising a plurality of training trajectories; (b) a second sequence of instructions which, when executed by the processor, causes the processor to perform a trajectory initialization; (c) a third sequence of instructions which, when executed by the processor, causes the processor to formulate off-line, a mathematical description of a constrained optimization problem for trajectory planning of a parallel kinematic machine (PKM), the mathematical description including a cost minimization function and augmented Lagrange multipliers utilized in an augmented Lagrange decoupling procedure (ALD) to transform the problem into a non-constrained problem, an inertia matrix invertibility condition control law specification, a discrete dynamic model approximation using a multi-step Adams predictive-corrective formulation initialized with a fourth order Runge-Kutta, and a stopping criteria, wherein an iterative solution to the optimization problem describes at least one optimized trajectory; (d) a fourth sequence of instructions which, when executed by the processor, causes the processor to save the at least one optimized trajectory; (e) a fifth sequence of instructions which, when executed by the processor, causes the processor to initialize membership function parameters defining fuzzy sets and number of rules for a Tsukamoto neuro-fuzzy inference procedure; (f) a sixth sequence of instructions which, when executed by the processor, causes the processor to optimize the membership function parameters for inputs extracted from the at least one optimized trajectory and outputs of the Tsukamoto neuro-fuzzy inference procedure; (g) a seventh sequence of instructions which, when executed by the processor, causes the processor to perform on-line the Tsukamoto neuro-fuzzy inference procedure to further optimize the trajectory of the PKM, the on-line Tsukamoto neuro-fuzzy inference procedure accepting Cartesian 2-dimensional positions and velocities as fuzzy inputs, and outputting joint torques and sampling periods representing the further optimization of the at least one optimized trajectory; (h) a eighth sequence of instructions which, when executed by the processor, causes the processor to transfer to the parallel kinetic machine a resultant trajectory planning program based on the further optimization; whereby the PKM executes motion consistent with the further optimization of the at least one optimized trajectory so that time and energy of the PKM motion is optimally minimized. 14. The computer software product according to claim 11 , further comprising: an eleventh sequence of instructions which, when executed by the processor, causes said processor to characterize a crisp EE position and velocity utilizing a 4-input, first neural layer; a twelfth sequence of instructions which, when executed by the processor, causes said processor to perform fuzzification of said crisp inputs into linguistic variables through Gaussian transfer functions utilizing a second neural layer; a thirteenth sequence of instructions which, when executed by the processor, causes said processor to apply a product T-norm to produce firing strengths of each rule utilizing a third rule defining neural layer; a fourteenth sequence of instructions which, when executed by the processor, causes said processor to normalize firing strengths by calculating a ratio of each rule's firing strength to a sum of all rules' firing strengths, said normalizing firing strengths occurring in a fourth neural layer; a fifteenth sequence of instructions which, when executed by the processor, causes said processor to invert results of said firing strength normalizing step in a fifth neural layer; and a sixteenth sequence of instructions which, when executed by the processor, causes said processor to aggregate and defuzzify results from said the inversion in the fifteenth sequence, said aggregating and defuzzifying occurring in a sixth neural layer providing crisp outputs comprised of said joint torques and said sampling periods.