Cc. Yih et Pi. Ro, NONLINEAR OPTIMIZATION-BASED MOTION PLANNING OF NONHOLONOMIC SYSTEMS USING AN ITERATIVE ALGORITHM, Intelligent automation and soft computing, 4(3), 1998, pp. 227-239
A nonlinear optimization-based scheme is developed for the motion plan
ning of nonholonomic systems. By specifying the final states constrain
ts and using the performance criteria involving the control energy, th
e motion planning of nonholonomic systems can be recast as a nonlinear
optimization problem which is to find suitable control inputs for ste
ering the system along a feasible path from an initial state to a fina
l stare. An iterative algorithm is proposed to solve for a feasible pa
th satisfying nonholonomic constraints and necessary optimality condit
ions. First, multi-point shooting is used to convert the motion planni
ng problem into the problem of finding the solution of nonlinear equat
ions. Modified Newton's method with line search is then used to ensure
the global convergence of the numerical algorithm. The proposed schem
e is applied to an one-leg hopping robot and a two-wheeled mobile robo
t. The results of numerical simulation clearly demonstrate the effecti
veness of the proposed motion planning scheme.