Method for Generating Trajectories for Motor Controlled Actuators
First Claim
1. A method for generating a trajectory for a motion controlled actuator, comprising the steps of:
- initializing data for solving a two-point boundary value problem (TBVP);
solving the TBVP associated with a first cost function that represents energy consumption of a motion control system using the data and an analytical solver to obtain an analytic solution for unconstrained motor optimal control subject to boundary condition (BC);
updating the BC and iterating beginning at the solving step if an acceleration constraint is violated;
otherwiseupdating the BC and iterating beginning at the solving step if a velocity constraint is violated; and
otherwisesetting the trajectory to the solution of the TBVP if the acceleration constraint and the velocity constraint are satisfied, wherein the steps are performed in a processor.
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Abstract
A method generates trajectories for motor controlled actuators subject to dynamics, acceleration and velocity constraints. The method solves a constrained optimal control problem with dynamics, acceleration, and velocity constraints. The motor control problem is formulated as an optimal control problem using an energy cost function which is based on numerical optimization results. A solution to the two-point boundary value problem (TBVP) for the unconstrained case of the optimal control problem is obtained. The energy efficient motor control trajectory generation solver is designed for real time energy efficient trajectory generation. The solver converts a difficult multi-point boundary value problem (MBVP) associated with the state and acceleration constrained optimal control problem into an iterative solution for the TBVPs with updated boundary conditions.
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Citations
14 Claims
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1. A method for generating a trajectory for a motion controlled actuator, comprising the steps of:
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initializing data for solving a two-point boundary value problem (TBVP); solving the TBVP associated with a first cost function that represents energy consumption of a motion control system using the data and an analytical solver to obtain an analytic solution for unconstrained motor optimal control subject to boundary condition (BC); updating the BC and iterating beginning at the solving step if an acceleration constraint is violated;
otherwiseupdating the BC and iterating beginning at the solving step if a velocity constraint is violated; and
otherwisesetting the trajectory to the solution of the TBVP if the acceleration constraint and the velocity constraint are satisfied, wherein the steps are performed in a processor. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A method for producing a minimum energy trajectory for motor control without going through the online numerical integration process. Rather, the integration is accomplished by matrix operations, which are inevitable to obtain the control time history. The matrices used in these matrix operations are computed off-line and stored for each time in a preselected time grid. Such a storage can be reused each time a new trajectory is computed, hence, this off-line computation arrangement help with reducing the amount of on-line computation.
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