Organizations: University of Wisconsin–Madison, WI, USA. · Shanghai Innovation Institute (SII), Shanghai, China
Abstract
We present a novel and minimalistic design of an aerial-terrestrial robot DASH: Ducted Aerial Spring Hopper. The goal is to enable both aerial and ground locomotion capabilities on a unified mobile robot that is mechanically-minimalistic, locomotion-versatile, and energy-efficient. We propose an organic integration of ducted fan co-axial body with a springy leg at the bottom for realization. The ducted fan module provides thrust-vectoring as the main actuation for agile flying; when it is combined with the light-weight spring leg, the robot realizes highly efficient ground hopping with energy circulation. Moreover, to realize optimal locomotion with two modes, we employ a contact-implicit model predictive controller to automatically choose locomotion modes and actuation. We successfully validated the design and control of DASH through a range of tasks, including periodic hopping, aerial flight, and mode-free locomotion with autonomous mode transitions during obstacle traversal.
In this work, we present Tilt-Ropter, a fully actuated hybrid aerial-terrestrial vehicle (HATV) that integrates tilt rotors with passive wheels to enable efficient multi-modal locomotion. Unlike conventional underactuated HATVs, the fully actuated design of Tilt-Ropter allows decoupled force and torque control, improving maneuverability and ground locomotion efficiency. A unified nonlinear model predictive controller (NMPC) is developed to track reference trajectories, enforce non-holonomic constraints, and accommodate contact effects across locomotion modes, while ensuring actuator feasibility through dedicated control allocation. To address complex wheel-ground dynamics, an external wrench estimator is incorporated to provide real-time interaction wrench estimates. The system is validated through simulation and real-world experiments, including seamless air-ground transitions and trajectory tracking tasks. Experimental results demonstrate low tracking errors in both modes and reveal a 92.8% reduction in power consumption during ground locomotion compared with flight, highlighting the platform's potential for long-duration missions where energy efficiency is critical.
Combining aerial thrust with spring-loaded hopping makes monopedal quadcopters promising for locomotion over complex terrain, but heuristic proportional-integral-derivative (PID) tuning limits coordination between active thrust and passive contact dynamics. We present a direct estimated-state-to-motor Proximal Policy Optimization (PPO) policy that commands four motors without an explicit hopping state machine or low-level attitude PID. Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping, which uses a history-aware power estimator to penalize general power use, impose an additional airborne-power cost, and penalize airborne near-stationarity. In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7% and mean total normalized thrust by 49.8% relative to the tuned PID-based control stack, while retaining repeatable commanded-height hopping and more concentrated landings. These observations are consistent with improved use of passive dynamics and reduced measured electrical demand.
Although aerial-legged robots offer combined agility and efficiency, controlling high-speed hopping under complex hybrid dynamics is challenging. Reinforcement Learning (RL) is promising but prone to energy-inefficient "reward hacking". We propose a Dynamics-Informed RL framework for a monopedal hopping quadcopter. By embedding a target Specific Energy into the reward, we constrain the optimization to a physically viable energy manifold, ensuring stable hopping behaviour. By rewarding the phase-consistent behavior, it can encourage bio-inspired stance-phase impulse. Furthermore, penalizing the electro-mechanical power waste induces the motors generate an efficient impulse. This enables the policy to inject energy strictly during spring restitution without heuristic state machines. MuJoCo simulations validate robust height regulation and forward velocity tracking up to 2.0 m/s despite severe attitude-contact coupling. Ultimately, our approach yields a highly agile hopping gait, reducing energy consumption by 82% and 73% compared to hovering baselines and inefficiency baseline, respectively.