The Journal of the Astronautical Sciences https://doi.org/10.1007/s40295-019-00171-6 Path Planning to a Reachable State Using Minimum Control Effort Based Navigation Functions Paul Quillen 1 · Josu ´ e Mu ˜ noz 2 · Kamesh Subbarao 1 © American Astronautical Society 2019 Abstract The purpose of this paper is to present a new path-planning algorithm for planetary exploration rovers that will guide the vehicle safely to a reachable state. In particular, this work will make use of a special class of artificial potential functions called navi- gation functions which are guaranteed to be free of local minimum. The construction of the navigation functions in this work is motivated by the grid-based wavefront expansion method but differs in that the contour levels are defined in terms of the control effort of the system. Two new methods will be introduced in this paper for defining the navigation function. The first method will generate a minimum con- trol effort path plan and the second method will be based on an inverse dynamics approach. Each of the control effort based methods will generate a path plan that will guide the rover’s approach towards an objective reachable state. Finally, a stable backstepping-like controller is implemented to track a trajectory defined along the path plan to the rover’s objective. Keywords Navigation function · Path planning · Unmanned rovers · Backstepping Introduction Path planning and control are a major part of any planetary exploration mission involving autonomous rovers. The rovers need to have a sense of autonomy due to the  Kamesh Subbarao subbarao@uta.edu Paul Quillen paul.quillen@mavs.uta.edu Josu´ e Mu˜ noz josue.munoz@us.af.mil 1 The University of Texas at Arlington, Arlington, TX 76019, USA 2 Flight Dynamics and Control Group, Air Force Research Laboratory/RVES, Albuquerque, NM, USA