Learning from Elephants: Trajectory Planning via Kinematic Invariants

Adaptive trajectory planning remains a central challenge in robotics, requiring solutions that integrate precision and generalizability. Derived from elephant trunk movements, this study introduces a novel trajectory planner for point reaching that builds upon biological demonstrations and satisfies kinematic invariants governing these movements. A Learning from Demonstration framework is designed to enable the extraction of reference trajectories from multiple demonstrations for different targets and their generalization to novel positions. In addition, we prove that the elephant trunk movements are governed by a generalized power law that relates the tangential velocity along a trajectory to a combination of its local curvature and torsion. Thus, this kinematic invariant is integrated into the planner design to ensure that generated trajectories are biologically faithful as well as capable of adapting to diverse goal positions.