Optimized Kalman Filter based State Estimation and Height Control in Hopping Robots

Quadrotor-based multimodal hopping and flying locomotion significantly improves efficiency and operation time as compared to purely flying systems. However, effective control necessitates continuous estimation of the vertical states. A single hopping state estimator has been shown (Kang 2024), in which two vertical states (position, acceleration) are measured and only velocity is estimated using a moving horizon estimation and visual inertial odometry at 200 Hz. This technique requires complex sensors (IMU, lidar, depth camera, contact force sensor), and computationally intensive calculations (12-core, 5 GHz processor), for a maximum hop height of $\sim$0.6 m at 3.65 kg. Here we show a trained Kalman filter based hopping vertical state estimator (HVSE), requiring only vertical acceleration measurements. Our results show the HVSE can estimate more states (position, velocity) with a mean-absolute-error in the hop apex ratio (height error/ground truth) of 12.5\%, running $\sim$4.2x faster (840 Hz) on a substantially less powerful processor (dual-core 240 MHz) with over $\sim$6.7x the hopping height (4.02 m) at 20\% of the mass (672 g). The presented general HVSE, and training procedure are broadly applicable to jumping, hopping, and legged robots across a wide range of sizes and hopping heights.