This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.

The decline of natural pollinators necessitates the development of novel pollination technologies. In this work, we propose a drone-enabled autonomous pollination system (APS) that consists of five primary modules: environment sensing, flower perception, path planning, flight control, and pollination mechanisms. These modules are highly dependent upon each other, with each module relying on inputs from the other modules. In this paper, we focus on approaches to the flower perception, path planning, and flight control modules. First, we briefly introduce a flower perception method from our previous work to create a map of flower locations. With a map of flowers, APS path planning is defined as a variant of the Travelling Salesman Problem (TSP). Two path planning approaches are compared based on mixed-integer programming (MIP) and genetic algorithms (GA), respectively. The GA approach is chosen as the superior approach due to the vast computational savings with negligible loss of optimality. To accurately follow the generated path for pollination, we develop a convex optimization approach to the quadrotor flight control problem (QFCP). This approach solves two convex problems. The first problem is a convexified three degree-of-freedom QFCP. The solution to this problem is used as an initial guess to the second convex problem, which is a linearized six degree-of-freedom QFCP. It is found that changing the objective of the second convex problem to minimize the deviation from the initial guess provides improved physical feasibility and solutions similar to a general-purpose optimizer. The path planning and flight control approaches are then tested within a model predictive control (MPC) framework where significant computational savings and embedded adjustments to uncertainty are observed. Coupling the two modules together provides a simple demonstration of how the entire APS will operate in practice.