This body of work presents methods for the optimization, analysis, and control of mixed serial-parallel structures known as SP-Stacks. A SP-Stack is a series of Stewart Platforms (SPs) linked via their top and bottom plates to create a serial chain of parallel mechanisms. SP-Stacks are unique in their bridging of the benefits of parallel architectures (high rigidity, strength, and precision) and serial architectures (reach and manipulability), at the cost of being extremely overactuated. SP-Stacks are also difficult to provide kinematic solutions for, as neither forward nor inverse kinematics of a system are closed form.
The first work presented focuses on presenting algorithms and optimization functions pertaining to the kinematic configuration of a SP-Stack. It first presents two methods of fast inverse kinematics (IK) for the SP-Stack which do not take forces into account. The outputs of those more simplistic solvers as used as initial conditions for a Nonlinear Program (NLP) algorithm which optimizes the internal configuration of a SP-Stack such that the end effector (EE) plate remains at the desired location, and the maximal force experienced on any actuator is minimized.
The second work presented focuses on hardware testing some of the constituent algorithms and conclusions drawn from the first paper and determining methods of compensating for, in software, detected defects in hardware and hardware measurement systems. This work also demonstrates a different form of force-optimization - compliance control (CC), which is executed on both a single SP responding to external forces, and a 2 SP-Stack responding to regular internal perturbation.
Conclusions drawn from these works are useful for stacks of an arbitrary number of SPs, can be extended to other mixed-kinematic systems, and advance the capabilities of these systems to be useful contributors in field robotics. / Master of Science / A stewart platform (SP) is a type of robot which consists of two plates interconnected by six linear actuators in parallel, which allow the robot to either translate or rotate about any axis in space. SPs are limited in their ability to move, as their parallel construction limits their workspace. In order to counteract this, SPs can be stacked on top of one another, creating a SP-Stack. The SP-Stack is capable of using its status as a mixed serial-parallel system to move in a significantly larger area (an advantage derived by the serial component of its architecture) and retain extraordinary rigidity and strength (an advantage from its parallel architecture).
As each SP has 6 Degrees of Freedom (6DoF), enabling the previously described free-space motion, a SP-Stack possesses 6n DoF, making it overactuated. An overactuated system has multiple internal configurations which allow for a desired end effector configuration. The body of work presented herein focuses on manipulating the overactuation of SP-Stacks to achieve desirable results such as finding configurations which are most resistant to external loading (optimization of actuator forces) or algorithms which allow SP-Stacks to comply with external loading (compliance control (CC)).
The first work presented herein focuses on determining an optimal configuration for a 4 SP-Stack such that the maximum force experienced by any one of its linear actuators is minimized, given a known external force. This work also presents two methods of generating initial configurations for the SP-Stack which are fed into the optimization algorithm which produces the final solution, as well as providing details on the constraints which govern the movement and validity of configurations for the system.
The second work presented expands on the work done in the first, moving into hardware testing for verification of algorithms which calculate forces experienced by the linear actuators. The hardware testing showcases some errors that can be introduced by low fidelity hardware, along with methodologies for counteracting those errors. Finally, the second work introduces CC, the ability for a robot to move itself to adapt to incoming forces, and applies it to a physical 2 SP-Stack as a demonstrator.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/113223 |
| Date | 17 January 2023 |
| Creators | Chapin, William Douglas |
| Contributors | Computer Science and Applications, Komendera, Erik, Karpatne, Anuj, Feng, Wu-chun |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | Creative Commons Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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