Optimal dynamic motion planning for underactuated robots

The modeling and control of underactuated robotic manipulators provide several challenges. Many of these systems would benefit from a reliable algorithm for producing motions that are optimal for performance measures like effort, power or time. In this dissertation we develop an algorithm for solving optimal motion planning problems for these systems. A local solution to the nonlinear optimal control problem is obtained using a constrained parameter optimization procedure. As part of this algorithm, a recursive dynamics formulation for underactuated serial chains is derived using matrix exponentials and the geometric framework provided by Lie groups and Lie algebras. This work builds upon previous work for fully actuated chains, but the solution is more difficult due to the presence of passive joints.; Due to the ill-conditioned nature of the optimization problem, we found that analytic gradient information was essential to achieve good convergence from the optimization software. One benefit of this matrix exponential formulation is the ability to easily derive the dynamic sensitivity equations. A recursive algorithm for computing the dynamic sensitivity equations with respect to joint positions, velocities, accelerations and torques is presented in this thesis. The nonlinear sensitivity equations are integrated forward in time in order to supply the optimization software with exact gradient information for a wide range of cost functions. The ability to use these gradients in the solution of motion optimization problems while keeping the full dynamic model is unique to our work.; The recursive dynamics and gradient algorithms are integrated into a Matlab package called C-Storm (Computer Simulation Tool for the Optimization of Robot Motions). Mex files are used to interface C++ dynamics code with the Matlab environment. C-Storm allows the user to easily create and model different robotic systems in a familiar, user friendly environment. Matlab also provides the necessary integration and parameter optimization software used to generate optimal motions. Several examples of optimal motions found using the C-Storm software package are presented.