Holonomic Vehicle Boundary Value Solver
Explicit solutions to the problem of point-to-point navigation of a holonomic vehicle operating within an obstacle-free world are straightforward. More specifically, a 6-degrees of freedom (DOF) vehicle that can be approximated to assume only small roll and pitch angles can be approximated using a very simple Boundary Value Solver (BVS). Considering an approximate state vector ξ = [x,y,z,ψ] (where x,y,z are the 3 position states and ψ the yaw angle), the path from the state configuration ξ0 to ξ1 is given by:
And considering a limitation on the possible rate of change of the yaw angle \dψ/dt|max and the maximum linear velocity υmax, the execution time is:
with d used to denote the Euclidean distance.