High Accuracy Aerial Maneuvers on Legged Robots using Variational Integrator Discretized Trajectory Optimization

Performing acrobatic maneuvers involving long aerial phases, such as precise dives or multiple backflips from significant heights, remains an open challenge in legged robot autonomy. Such aggressive motions often require accurate state predictions over long horizons with multiple contacts and extended flight phases. Most existing trajectory optimization (TO) methods rely on Euler or Runge-Kutta integration, which can accumulate significant prediction errors over long planning horizons. In this work, we propose a novel whole-body TO method using variational integration (VI) and full-body nonlinear dynamics for long-flight aggressive maneuvers. Compared to traditional Euler-based TO, our approach using VI preserves energy and momentum properties of the continuous-time system and reduces error between predicted and executed trajectories by factors of between 2 - 10 while achieving similar planning time. We successfully demonstrate long-flight triple backflips on a quadruped A1 robot model and backflips on a bipedal HECTOR robot model for various heights and distances, achieving landing angle errors of only a few degrees. In contrast, TO with Euler integration fails to achieve accurate landings in equivalent circumstances, e.g., with landing angle errors greater than 90° for triple backflips. We provide an open-source implementation of our VI -discretized TO to support further research on accurate dynamic maneuvers for multi-rigid-body robot systems with contact: https://github.com/DRCL-USC/VI_discretized_TO