CONTROL METHOD FOR MOBILE PARALLEL MANIPULATORS
First Claim
1. A computer-implemented control method for a mobile parallel manipulator (MPM), comprising the steps of:
- (a) setting trajectory parameters in an offline dataset, the trajectory parameters including initial and final positions, limits on state components, strut lengths, torques, accelerations, and sampling periods;
(b) formulating, off-line, a mathematical description of a constrained optimization problem for trajectory planning of the mobile parallel manipulator (MPM), the mathematical description including;
an energy and time cost minimization function and augmented Lagrange multipliers utilized in an augmented Lagrange decoupling procedure (ALD) to transform the problem into a non-constrained problem, the energy and time cost minimization function including inputs describing;
(i) a moving coordinate system related to self-movement of a base of the MPM relative to a fixed reference frame; and
(ii) torques and angular positions of actuators coupled to an end plate of the MPM;
an inertia matrix invertibility condition control law specification;
a discrete dynamic model approximation using a multi-step Adams-Bashforth predictive-corrective formulation;
a stopping criteria, wherein an iterative solution to the optimization problem describes at least one optimized trajectory;
(c) saving the at least one optimized trajectory;
(d) deriving at least one inverse kinematic solution based on the at least one optimized trajectory, wherein a joint position characterized by coordinates (q1, q2, q3, q4, q5) is found from Cartesian coordinates (x, y, z, φ
);
(e) formulating, on-line, an optimized forward kinematic solution based on the at least one inverse kinematic solution;
(f) transferring to the MPM a resultant trajectory plan based on the optimized forward kinematic solution; and
(g) controlling the MPM actuators to constrain the MPM to execute motion consistent with the at least one optimized trajectory so that time, energy, and, alternatively, time and energy of the MPM motion is optimally minimized.
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Abstract
In the control method for mobile parallel manipulators, kinematic singularity and redundancy are solved through joint limits avoidance and manipulability criteria. By taking the MPM self-motion into consideration due to its redundancy, the inverse kinematic is derived using a hybrid neuro-fuzzy system, such as NeFIK. The discrete augmented Lagrangian (AL) technique is used to solve the highly nonlinear constrained multi-objective optimal control problem. An adaptive neuro-fuzzy inference system (ANFIS)-based structure (based on the result of the AL solution) is used to solve the online trajectory planning of the MPM.
14 Citations
20 Claims
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1. A computer-implemented control method for a mobile parallel manipulator (MPM), comprising the steps of:
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(a) setting trajectory parameters in an offline dataset, the trajectory parameters including initial and final positions, limits on state components, strut lengths, torques, accelerations, and sampling periods; (b) formulating, off-line, a mathematical description of a constrained optimization problem for trajectory planning of the mobile parallel manipulator (MPM), the mathematical description including; an energy and time cost minimization function and augmented Lagrange multipliers utilized in an augmented Lagrange decoupling procedure (ALD) to transform the problem into a non-constrained problem, the energy and time cost minimization function including inputs describing; (i) a moving coordinate system related to self-movement of a base of the MPM relative to a fixed reference frame; and (ii) torques and angular positions of actuators coupled to an end plate of the MPM; an inertia matrix invertibility condition control law specification; a discrete dynamic model approximation using a multi-step Adams-Bashforth predictive-corrective formulation; a stopping criteria, wherein an iterative solution to the optimization problem describes at least one optimized trajectory; (c) saving the at least one optimized trajectory; (d) deriving at least one inverse kinematic solution based on the at least one optimized trajectory, wherein a joint position characterized by coordinates (q1, q2, q3, q4, q5) is found from Cartesian coordinates (x, y, z, φ
);(e) formulating, on-line, an optimized forward kinematic solution based on the at least one inverse kinematic solution; (f) transferring to the MPM a resultant trajectory plan based on the optimized forward kinematic solution; and (g) controlling the MPM actuators to constrain the MPM to execute motion consistent with the at least one optimized trajectory so that time, energy, and, alternatively, time and energy of the MPM motion is optimally minimized. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A computer software product, comprising a non-transitory medium readable by a processor, the non-transitory medium having stored thereon a set of instructions for performing a control method for a mobile parallel manipulator, the set of instructions including:
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(a) a first sequence of instructions which, when executed by the processor, causes said processor to set trajectory parameters in an offline dataset, said trajectory parameters including initial and final positions, limits on state components, strut lengths, torques, accelerations, and sampling periods; (b) a second sequence of instructions which, when executed by the processor, causes said processor to formulate, off-line, a mathematical description of a constrained optimization problem for trajectory planning of said mobile parallel manipulator (MPM), the mathematical description including; an energy and time cost minimization function and augmented Lagrange multipliers utilized in an augmented Lagrange decoupling procedure (ALD) to transform the problem into a non-constrained problem, said energy and time cost minimization function including inputs describing (i) a moving coordinate system related to self-movement of a base of said MPM relative to a fixed reference frame and (ii) torques and angular positions of actuators coupled to an end plate of said MPM; an inertia matrix invertibility condition control law specification; a discrete dynamic model approximation using a multi-step Adams-Bashforth predictive-corrective formulation; a stopping criteria, wherein an iterative solution to the optimization problem describes at least one optimized trajectory; (c) a third sequence of instructions which, when executed by the processor, causes said processor to save the at least one optimized trajectory; (d) a fourth sequence of instructions which, when executed by the processor, causes said processor to derive at least one inverse kinematic solution based on said at least one optimized trajectory wherein a joint position characterized by coordinates (q1, q2, q3, q4, q5) is found from Cartesian coordinates (x, y, z, φ
);(e) a fifth sequence of instructions which, when executed by the processor, causes said processor to formulate, on-line, an optimized forward kinematic solution based on said at least one inverse kinematic solution; (f) a sixth sequence of instructions which, when executed by the processor, causes said processor to transfer to the MPM a resultant trajectory plan based on said optimized forward kinematic solution; and (g) a seventh sequence of instructions which, when executed by the processor, causes said processor to control said MPM actuators, wherein said MPM executes motion consistent with the at least one optimized trajectory so that time, energy, and alternatively time and energy of the MPM motion is optimally minimized. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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Specification