Patent Document ID: 8719212
Application ID: 13103950

Base Claim:
1. A computer-implemented parallel kinematic machine trajectory planning method, comprising the steps of: (a) selecting new trajectory parameters from an offline dataset having a plurality of training trajectories; (b) performing a trajectory initialization; (c) formulating, 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) saving the at least one optimized trajectory; (e) initializing membership function parameters defining fuzzy sets and number of rules for a Tsukamoto neuro-fuzzy inference procedure; (f) optimizing the membership function parameters for inputs extracted from the at least one optimized trajectory and outputs of the Tsukamoto neuro-fuzzy inference procedure; (g) performing 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 further optimization of the at least one optimized trajectory; and (h) transferring 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.

---

Claim 4:
4. The computer-implemented parallel kinematic machine trajectory planning method according to claim 1 , wherein the step of performing the Tsukamoto neuro-fuzzy inference procedure further comprises the steps of: characterizing a crisp end effector (EE) position and velocity utilizing a 4-input, first neural layer; performing fuzzification of the crisp inputs into linguistic variables through Gaussian transfer functions utilizing a second neural layer; applying a product T-norm to produce firing strengths of each rule utilizing a third rule-defining neural layer; normalizing firing strengths by calculating a ratio of each rule's firing strength to a sum of all rules' firing strengths, the normalizing firing strengths occurring in a fourth neural layer; inverting results of the firing strength normalizing step in a fifth neural layer; and aggregating and defuzzifying results from the inverting step, the aggregating and defuzzifying occurring in a sixth neural layer providing crisp outputs including joint torques and sampling periods.