Methods for Kinematic Analysis and Optimization of Overactuated Serial and Parallel Structures

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.