Bio-inspired Thrust-Assisted Trotting on a legged-Aerial Robot via Real-Time QP-MPC

Shreyansh Pitroda; Eric Sihite; Alireza Ramezani; Morteza Gharib

cs.ROOct 19, 2026

Bio-inspired Thrust-Assisted Trotting on a legged-Aerial Robot via Real-Time QP-MPC

Authors: Shreyansh Pitroda, Eric Sihite, Alireza Ramezani, Morteza Gharib

Organizations: The authors are with SiliconeSynapse Labs, the Department of Electrical Engineering, Northeastern University, USA. · The authors are with the Department of Aerospace Engineering, California Institute of Technology, USA.

Abstract

This paper presents the hardware implementation of a quadratic program-based controller on Harpy: thruster-assisted bipedal robot to perform thruster-assisted trotting. This is inspired by wing-assisted locomotion observed in birds such as the chukar partridge, which employ thrust vectoring to manipulate the ground reaction force. The proposed controller formulates the thruster-assisted spring-loaded inverted pendulum dynamics as a condensed QP-based model predictive control problem, enabling simultaneous regulation of ground contact force and active thrust vectoring at 500 Hz. A decoupled control architecture is used, where the robot's sagittal dynamics are controlled using QP-MPC while the frontal dynamics is regulated using a cascade orientation stabilization controller. Two experiments were conducted with different forward reference velocities of 0 m/s and 0.1 m/s. While the instantaneous velocity oscillates, the mean velocities can track their respective reference. Additionally, joint tracking error remains within 1 deg while tracking the desired leg length given by the leg trajectory controller and desired swing trajectory given by Raibert's heuristic. The QP-MPC problem is consistently solved with 0.18ms, which is well within the 2ms computation budget while satisfying the GRF friction cone constraint.

Figures & tables

Fig. 1: Illustrates biological inspiration for thruster-assisted bipedal robot. Birds employ wing-assisted locomotion to manipulate GRF [ 2 ] . Harpy replicates this strategy by replacing biological wings with electric ducted fans, enabling active thrust vectoring.

Fig. 2: (Left) Full-order kinematic model of our robot highlighting joint, and thruster position. (Right) Planar 2D Spring-loaded Inverted Pendulum reduced-order model used for QP-MPC formulation.

PWM	Side thruster	Upper thruster
(%)	(kgf)	(kgf)
10	0.092	0.0875
20	0.37	0.175
30	0.809	0.2625
40	1.346	0.35
50	1.97	0.4375

TABLE I: Mapping PWM to thruster forces

Fig. 3: Control architecture of the proposed QP-TSLIP controller.

Fig. 4: Sequential snapshots from hardware Experiment B. The robot performs thruster-assisted trotting locomotion using the proposed QP-TSLIP controller.

Fig. 5: Illustrates QP solver performance on hardware. (Left) Histogram of QP total computation time for Experiment A (blue) and Experiment B (red). (Right) Distribution of solver iteration, displaying majority convergence within 6-7 steps.

Fig. 6: Illustrates GRF distribution within the friction cone for Experiment A (Left) and Experiment B (Right). Each point represents the horizontal and vertical force commanded by the QP solver, colored by time (cyan = start and magenta = end). The red line denotes the friction cone boundary with coefficient $\mu=0.5$ .

Fig. 7: Thruster force commands during hardware experiments. (Top) QP-commanded forward thrust $~u_{t,x}$ for both the experiments. The thrust frequently remains near the saturation limit of $\pm 8.7~\text{N}$ . (Bottom-left) Side thruster forces for Experiment A and (Bottom-right) for Experiment B, showing left and right thruster output combining PID orientation controller and QP controller. The dashed line at 5N denotes the baseline produced by the QP controller.

Fig. 8: Body state trajectory during hardware experiments. (Top-left) COM position in x-direction for Experiment A (blue) and Experiment B (red) with dotted position reference line (black). (Top-right) body velocity in the x-direction, along with the mean values and velocity reference. (Bottom-left) Pitch angle remains bounded within $\pm 9^{\circ}$ throughout both experiments. (Bottom-right) Roll angle stays within $\pm 4^{\circ}$ , validating the effectiveness of the cascade control strategy. The filled black circle $(\bullet)$ denotes the end of Experiment B.

Fig. 9: Box plot for joint trajectory tracking error for Experiment A and Experiment B.

Fig. 10: MPC prediction rollout validated on hardware for Experiment A. Forward (top-left), and vertical (Bottom-left) COM velocity trajectory comparing the QP-MPC model prediction against the hardware measurement (blue). The zoomed section illustrates the receding horizon strategy where at each state feedback point (red dot), the linearized SLIP model rollout (black) are calculated for 5 horizon.

Robot Locomotion

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Anti-Gravity Walking by a Flying Humanoid Robot via Thrust-Rate Input Whole-Body Model Predictive Control

Kazuki Sugihara, Kei Okada

Department of Mechano-Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Aerial Robotics Humanoid Robot Locomotion Model Predictive Control

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Flying humanoids are expected to perform tasks in diverse environments, while their existing locomotion is mainly limited to aerial flight and ground walking. The capability to move in complex three-dimensional space can greatly expand their application range. For such walking motion on ceilings and similar anti-gravity environments, whole-body MPC is effective. However, the discontinuous changes in dynamic structure accompanying contact switching during walking can induce thrust spikes, resulting in control instability. Therefore, in this work, we propose and implement a real-time whole-body MPC framework for anti-gravity bipedal walking. First, we formulate whole-body MPC using the time derivative of thrust, namely thrust-rate, as the control input. This formulation guarantees continuity of the thrust trajectory during contact switching while preserving the sparse structure of the optimal control problem for fast computation. Second, we address the lack of natural support forces in anti-gravity environments. We introduce lower bounds on the foot-normal component of the contact force, and smoothly transfer them during the doublesupport phase. Finally, we implement the proposed framework and demonstrate anti-gravity walking by a flying humanoid through simulation and a hardware experiment. To the best of our knowledge, this is the first demonstration of multi-contact whole-body MPC for a transformable aerial robot and walking by a flying humanoid beyond the ground.

Abstract

Robot Locomotion

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