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# Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

- Saturday, 01 September 2012

### A method is investigated how to maximize energy transfer to tools used in drilling, and can be applied to regular power tools.

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy).

Planetary Rover equipped with a rotary percussive drill." class="caption" align="right">To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein.

To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both openloop and closed-loop control modes (using standard real-time control hardware).

Future NASA *in situ* exploration missions
increasingly require extensive
drilling and coring procedures that
stress the demand for more energy efficient
methods to accomplish these tasks.
For example, when rover-based autonomous drills are controlled non-optimally
for long periods of time, the energy
loss can grow at a rate that cannot be sustained
by the rover’s internal energy supply.
Motorized percussive units can be
especially energy-draining (when controlled
non-optimally), making this technology
especially relevant to this type of
future NASA work.

*This work was done by Jack B. Aldrich and
Avi B. Okon of Caltech for NASA’s Jet
Propulsion Laboratory. NPO-48467*

### This Brief includes a Technical Support Package (TSP).

** Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications** (reference NPO-48467) is currently available for download from the TSP library.

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