Inspired by fast model predictive control (MPC), a new nonlinear optimal command tracking technique is presented in this paper, which is named as “Tracking-oriented Model Predictive Static Programming (T-MPSP).” Like MPC, a model-based prediction-correction approach is adopted. However, the entire problem is converted to a very low-dimensional “static programming” problem from which the control history update is computed in closed-form. Moreover, the necessary sensitivity matrices (which are the backbone of the algorithm) are computed recursively. These two salient features make the computational process highly efficient, thereby making it suitable for implementation in real time. A trajectory tracking problem of a two-wheel differential drive mobile robot is presented to validate and demonstrate the proposed philosophy. The simulation studies are very close to realistic scenario by incorporating disturbance input, parameter uncertainty, feedback sensor noise, time delays, state constraints, and control constraints. The algorithm has been implemented on a real hardware and the experimental validation corroborates the simulation results.
A lead angle constrained optimal mid course guidance in this paper, which is quite important for missions with missiles with limited sensor capability to detect and monitor the target. This guidance law not only achieves the minimum control effort, but also generates the desired optimal terminal angles (in both pitch and yaw planes) that can lead to proper trajectory shaping to assure the desired lead angle during the midcourse. If both plane terminal lead angles are free, then this guidance will generate the desired terminal lead angles such that control effort can be minimized. If total lead angle is specified, then this guidance law solves the constraint optimal problem to find the lead angles in both plane optimally. In a case where both lead angles are specified, this guidance law will achieves this with minimum control effort. For all the three cases close form solutions for the lateral acceleration command has been obtained. Simulation results for all three cases are quite very promising. Robustness and generalized nature of this guidance law have also been demonstrated through extensive simulations in this paper.
Using the recently proposed computationally efficient model predictive static programming (MPSP), a suboptimal guidance law is presented in this paper for guidance of small range tactical surface-to-surface missiles satisfying both way-point as well as terminal impact angle constraints. The guidance law also satisfies terminal lateral acceleration constraint, and hence, it indirectly satisfies terminal body angle constraint as well. Way-point constraint gives the flexibility to shape the trajectory as well as to deceive the enemy by giving an impression that it is targeted elsewhere until the very last moment, thereby denying the enemy a long reaction time. The MPSP guidance law is primarily based on nonlinear optimal control theory and hence imbed effective trajectory optimization concepts into the guidance law. The computational requirement by the MPSP guidance is quite small and hence the necessary trajectory optimization is done in the onboard processor in real time. This throws the possibility of dynamically changing the way points onboard if necessary, which can serve as an effective additional counter measure strategy, without compromising on the terminal position and angle accuracies.
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