Planning $$ {{\mathbb{G}}^3} $$ -continuous paths for state-constrained mobile robots with bounded curvature of motion

A G3-Continuous Extend Procedure for Path Planning of Mobile Robots with Limited Motion Curvature and State Constraints

“…According to Equation (2), this implies thatβ is continuous. Sinceβ is related to curvature κ(t) by Equation (4), one concludes that admissible trajectories of the carlike kinematics must have curvature κ(t) of class C 1 (with a continuous time derivative), which satisfies Equation (3). As a consequence of such requirements, admissible paths for the carlike kinematics must be G 3 -continuous, that is, for a pathq ds (s f in ) = 0.…”

“…It is also important to maintain a high degree of path continuity to achieve smooth control of the robot and increase the comfort of passengers or the safety of the payload. To account for all these constraints, we built upon our approach introduced in Reference [3], where we proposed the extend procedure generating G 3 -continuous planar paths (that is, paths with continuous curvature derivative with respect to curve arc length) taking into account a limited curvature of motion in cluttered environments. In contrast to Reference [3], we present the new extend procedure for the carlike kinematics taking into account vehicle-body dimensions in planning collision-free paths, admitting the nonconvex polygonal obstacles present in the operational space.…”

“…To account for all these constraints, we built upon our approach introduced in Reference [3], where we proposed the extend procedure generating G 3 -continuous planar paths (that is, paths with continuous curvature derivative with respect to curve arc length) taking into account a limited curvature of motion in cluttered environments. In contrast to Reference [3], we present the new extend procedure for the carlike kinematics taking into account vehicle-body dimensions in planning collision-free paths, admitting the nonconvex polygonal obstacles present in the operational space. As a consequence, the motion-planning strategy presented in the current paper inherits beneficial properties of the original approach presented in Reference [3], but extends its potential applications to more practical path-planning scenarios.…”

“…In contrast to Reference [3], we present the new extend procedure for the carlike kinematics taking into account vehicle-body dimensions in planning collision-free paths, admitting the nonconvex polygonal obstacles present in the operational space. As a consequence, the motion-planning strategy presented in the current paper inherits beneficial properties of the original approach presented in Reference [3], but extends its potential applications to more practical path-planning scenarios.…”