Abstract
This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.
Highlights
Predicts the trajectory of a nonlinear closed-loop system; Works in real-time using a specified time horizon; Uses a feedback linearization control law to reduce the nonconvexity of the optimization problem; Supports state and input constraints of the closed-loop system, and is able to account for environmental constraints such as dynamic obstacles; Assumes that a stable terminal point is specified, and the state vector of the closed-loop system is available, and provides a combination of stabilization and tracking functionality:
This paper proposed a novel reference trajectory generation method for a nonlinear closed-loop system based on the Nonlinear Model Predictive Control (NMPC) approach
The proposed formulation, called Nonlinear Model Predictive Horizon (NMPH), applies a feedback linearization control law to the nonlinear plant model, resulting in a closed-loop dynamics model with decreased nonconvexity used by the online optimization problem to generate feasible and optimal reference trajectories for the actual closed-loop system
Summary
Estimates the system states from previous measurements over the estimation horizon. Plans an optimal reference trajectory for the system under an existing feedback control design. Dynamic OP is solved iteratively for the optimal control inputs over the prediction horizon. Dynamic OP is solved iteratively for the optimal trajectory over the given prediction horizon. A quadratic function which penalizes deviations of the predicted system states and control inputs. Composed of a stage cost and a terminal cost. A quadratic function which penalizes deviations of the estimated outputs from the measured outputs. Composed of an arrival cost and a stage cost. Quadratic function which penalizes the deviation of the predicted system states and reference trajectory. Relies on the accuracy of the system model, stability of closed-loop system, and accuracy of the initial state estimate
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