Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems

It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized matrix inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

Minimal-Sensing, Passive Force Identification Techniques for a Composite Structural Missile Component

Structural health monitoring systems are often limited to the use of one sensor due to cost, complexity, and weight restrictions. Therefore, there is a need to develop load and damage identification techniques that utilize only one sensor. Two passive force estimation techniques are investigated in this work. The techniques focus on either the shape or the amplitude of the magnitude of the applied force in the frequency domain. Both techniques iteratively reduce an underdetermined set of equations of motion into many overdetermined systems of equations to solve for the force estimates. The techniques are shown to locate and quantify impulsive impacts with over 97% accuracy and non-impulsive impacts with at least 87% accuracy. A filament-wound rocket motor casing is used as a test structure. Impacts not acting at a specific input degree of freedom are also accurately located depending on the distance away from the modeled input degrees of freedom, and damaging impact forces are quantified by making assumptions about the impulsive nature of the applied force.

Inference of velocity pattern from isochronous layers in firn, using an inverse method

The suitability of a kinematic approach for finding the velocity field from dated internal-layer architecture in firn is investigated. Internal layers are isochrones and the depositional age of a layer particle is treated as a tracer. The forward problem uses two-dimensional steady-state advection of age and conservation of mass to predict layer architecture. Different combinations of constraints on horizontal and vertical velocity properties are added. The inverse problem can be formulated as the solution of underdetermined and overdetermined systems of equations. The systems are solved using singular-value decomposition, allowing analysis of the singular-value spectrum, model resolution and data resolution. Solutions of the inverse problem are evaluated by comparing the velocity-field solutions with synthetic input velocity data. Unlike conventional accumulation estimates, the new approach takes lateral advection into account, enabling improved separation of spatial and temporal variations in accumulation. Two glaciological applications are presented: the determination of the migration velocity of a spatially non-stationary accumulation pattern and reconstruction of past accumulation and its stationarity over time.