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Integrating Trajectory Optimization and Reinforcement Learning for Quadrupedal Jumping with Terrain-Adaptive Landing

Wang, Renjie, Lyu, Shangke, Lang, Xin, Xiao, Wei, Wang, Donglin

arXiv.org Artificial Intelligence

Abstract-- Jumping constitutes an essential component of quadruped robots' locomotion capabilities, which includes dynamic take-off and adaptive landing. Existing quadrupedal jumping studies mainly focused on the stance and flight phase by assuming a flat landing ground, which is impractical in many real world cases. This work proposes a safe landing framework that achieves adaptive landing on rough terrains by combining Trajectory Optimization (TO) and Reinforcement Learning (RL) together . The RL agent learns to track the reference motion generated by TO in the environments with rough terrains. T o enable the learning of compliant landing skills on challenging terrains, a reward relaxation strategy is synthesized to encourage exploration during landing recovery period. Extensive experiments validate the accurate tracking and safe landing skills benefiting from our proposed method in various scenarios. I. INTRODUCTION With the development of the legged robot community over several decades, the locomotion performance of quadruped robots has improved remarkably, including but not limited to traversing the wild and performing robustly against disturbances [1], [2], [3], [4], [5], [6], [7], [8], [9].


Refining Motion for Peak Performance: Identifying Optimal Gait Parameters for Energy-Efficient Quadrupedal Bounding

Alqaham, Yasser G., Cheng, Jing, Gan, Zhenyu

arXiv.org Artificial Intelligence

Energy efficiency is a critical factor in the performance and autonomy of quadrupedal robots. While previous research has focused on mechanical design and actuation improvements, the impact of gait parameters on energetics has been less explored. In this paper, we hypothesize that gait parameters, specifically duty factor, phase shift, and stride duration, are key determinants of energy consumption in quadrupedal locomotion. To test this hypothesis, we modeled the Unitree A1 quadrupedal robot and developed a locomotion controller capable of independently adjusting these gait parameters. Simulations of bounding gaits were conducted in Gazebo across a range of gait parameters at three different speeds: low, medium, and high. Experimental tests were also performed to validate the simulation results. The findings demonstrate that optimizing gait parameters can lead to significant reductions in energy consumption, enhancing the overall efficiency of quadrupedal locomotion. This work contributes to the advancement of energy-efficient control strategies for legged robots, offering insights directly applicable to commercially available platforms.


16 Ways to Gallop: Energetics and Body Dynamics of High-Speed Quadrupedal Gaits

Alqaham, Yasser G., Cheng, Jing, Gan, Zhenyu

arXiv.org Artificial Intelligence

Galloping is a common high-speed gait in both animals and quadrupedal robots, yet its energetic characteristics remain insufficiently explored. This study systematically analyzes a large number of possible galloping gaits by categorizing them based on the number of flight phases per stride and the phase relationships between the front and rear legs, following Hildebrand's framework for asymmetrical gaits. Using the A1 quadrupedal robot from Unitree, we model galloping dynamics as a hybrid dynamical system and employ trajectory optimization (TO) to minimize the cost of transport (CoT) across a range of speeds. Our results reveal that rotary and transverse gallop footfall sequences exhibit no fundamental energetic difference, despite variations in body yaw and roll motion. However, the number of flight phases significantly impacts energy efficiency: galloping with no flight phases is optimal at lower speeds, whereas galloping with two flight phases minimizes energy consumption at higher speeds. We validate these findings using a quadratic programming (QP)-based controller, developed in our previous work, in Gazebo simulations. These insights advance the understanding of quadrupedal locomotion energetics and may inform future legged robot designs for adaptive, energy-efficient gait transitions.


Design and Control of A Tilt-Rotor Tailsitter Aircraft with Pivoting VTOL Capability

Ma, Ziqing, Smeur, Ewoud J. J., de Croon, Guido C. H. E.

arXiv.org Artificial Intelligence

-- T ailsitter aircraft attract considerable interest due to their capabilities of both agile hover and high speed forward flight. However, traditional tailsitters that use aerodynamic control surfaces face the challenge of limited control effectiveness and associated actuator saturation during vertical flight and transitions. Conversely, tailsitters relying solely on tilting rotors have the drawback of insufficient roll control authority in forward flight. This paper proposes a tilt-rotor tailsitter aircraft with both elevons and tilting rotors as a promising solution. By implementing a cascaded weighted least squares (WLS) based incremental nonlinear dynamic inversion (INDI) controller, the drone successfully achieved autonomous waypoint tracking in outdoor experiments at a cruise airspeed of 16 m/s, including transitions between forward flight and hover without actuator saturation. Wind tunnel experiments confirm improved roll control compared to tilt-rotor-only configurations, while comparative outdoor flight tests highlight the vehicle's superior control over elevon-only designs during critical phases such as vertical descent and transitions. Finally, we also show that the tilt-rotors allow for an autonomous takeoff and landing with a unique pivoting capability that demonstrates stability and robustness under wind disturbances. Index T erms-- VTOL aircraft, tailsitter UA V, incremental control, tilt rotors, autonomous flight.


Realtime Limb Trajectory Optimization for Humanoid Running Through Centroidal Angular Momentum Dynamics

Sovukluk, Sait, Schuller, Robert, Englsberger, Johannes, Ott, Christian

arXiv.org Artificial Intelligence

One of the essential aspects of humanoid robot running is determining the limb-swinging trajectories. During the flight phases, where the ground reaction forces are not available for regulation, the limb swinging trajectories are significant for the stability of the next stance phase. Due to the conservation of angular momentum, improper leg and arm swinging results in highly tilted and unsustainable body configurations at the next stance phase landing. In such cases, the robotic system fails to maintain locomotion independent of the stability of the center of mass trajectories. This problem is more apparent for fast and high flight time trajectories. This paper proposes a real-time nonlinear limb trajectory optimization problem for humanoid running. The optimization problem is tested on two different humanoid robot models, and the generated trajectories are verified using a running algorithm for both robots in a simulation environment.


A 3-Step Optimization Framework with Hybrid Models for a Humanoid Robot's Jump Motion

Qi, Haoxiang, Yu, Zhangguo, Chen, Xuechao, Liu, Yaliang, Yi, Chuanku, Dong, Chencheng, Meng, Fei, Huang, Qiang

arXiv.org Artificial Intelligence

High dynamic jump motions are challenging tasks for humanoid robots to achieve environment adaptation and obstacle crossing. The trajectory optimization is a practical method to achieve high-dynamic and explosive jumping. This paper proposes a 3-step trajectory optimization framework for generating a jump motion for a humanoid robot. To improve iteration speed and achieve ideal performance, the framework comprises three sub-optimizations. The first optimization incorporates momentum, inertia, and center of pressure (CoP), treating the robot as a static reaction momentum pendulum (SRMP) model to generate corresponding trajectories. The second optimization maps these trajectories to joint space using effective Quadratic Programming (QP) solvers. Finally, the third optimization generates whole-body joint trajectories utilizing trajectories generated by previous parts. With the combined consideration of momentum and inertia, the robot achieves agile forward jump motions. A simulation and experiments (Fig. \ref{Fig First page fig}) of forward jump with a distance of 1.0 m and 0.5 m height are presented in this paper, validating the applicability of the proposed framework.


Tethered Variable Inertial Attitude Control Mechanisms through a Modular Jumping Limbed Robot

Tanaka, Yusuke, Zhu, Alvin, Hong, Dennis

arXiv.org Artificial Intelligence

This paper presents the concept of a tethered variable inertial attitude control mechanism for a modular jumping-limbed robot designed for planetary exploration in low-gravity environments. The system, named SPLITTER, comprises two sub-10 kg quadrupedal robots connected by a tether, capable of executing successive jumping gaits and stabilizing in-flight using inertial morphing technology. Through model predictive control (MPC), attitude control was demonstrated by adjusting the limbs and tether length to modulate the system's principal moments of inertia. Our results indicate that this control strategy allows the robot to stabilize during flight phases without needing traditional flywheel-based systems or relying on aerodynamics, making the approach mass-efficient and ideal for small-scale planetary robots' successive jumps. The paper outlines the dynamics, MPC formulation for inertial morphing, actuator requirements, and simulation results, illustrating the potential of agile exploration for small-scale rovers in low-gravity environments like the Moon or asteroids.


Aviation Safety Enhancement via NLP & Deep Learning: Classifying Flight Phases in ATSB Safety Reports

Nanyonga, Aziida, Wasswa, Hassan, Wild, Graham

arXiv.org Artificial Intelligence

-- Aviation safety is paramount, demanding precise analysis of safety occurrences during different flight phases. This study employs Natural Language Processing (NLP) and Deep Learning models, including LSTM, CNN, Bidirectional LSTM (BLSTM), and simple Recur rent Neural Networks (sRNN), to classify flight phases in safety reports from the Australian Transport Safety Bureau (ATSB). The models exhibit ed high accuracy, precision, recall, and F1 scores, with LSTM achieving the highest performance of 87%, 88%, 87%, and 88%, respectively. This performance highlights their effectiveness in automating safety occurrence analysis. The integration of NLP and Deep Learning technologies promises transformative enhancements in aviation safety analysis, enabling targ eted safety measures and streamlined report handling.


Natural Language Processing and Deep Learning Models to Classify Phase of Flight in Aviation Safety Occurrences

Nanyonga, Aziida, Wasswa, Hassan, Molloy, Oleksandra, Turhan, Ugur, Wild, Graham

arXiv.org Artificial Intelligence

The air transport system recognizes the criticality of safety, as even minor anomalies can have severe consequences. Reporting accidents and incidents play a vital role in identifying their causes and proposing safety recommendations. However, the narratives describing pre-accident events are presented in unstructured text that is not easily understood by computer systems. Classifying and categorizing safety occurrences based on these narratives can support informed decision-making by aviation industry stakeholders. In this study, researchers applied natural language processing (NLP) and artificial intelligence (AI) models to process text narratives to classify the flight phases of safety occurrences. The classification performance of two deep learning models, ResNet and sRNN was evaluated, using an initial dataset of 27,000 safety occurrence reports from the NTSB. The results demonstrated good performance, with both models achieving an accuracy exceeding 68%, well above the random guess rate of 14% for a seven-class classification problem. The models also exhibited high precision, recall, and F1 scores. The sRNN model greatly outperformed the simplified ResNet model architecture used in this study. These findings indicate that NLP and deep learning models can infer the flight phase from raw text narratives, enabling effective analysis of safety occurrences.


Mastering Agile Jumping Skills from Simple Practices with Iterative Learning Control

Nguyen, Chuong, Bao, Lingfan, Nguyen, Quan

arXiv.org Artificial Intelligence

Achieving precise target jumping with legged robots poses a significant challenge due to the long flight phase and the uncertainties inherent in contact dynamics and hardware. Forcefully attempting these agile motions on hardware could result in severe failures and potential damage. Motivated by these challenging problems, we propose an Iterative Learning Control (ILC) approach that aims to learn and refine jumping skills from easy to difficult, instead of directly learning these challenging tasks. We verify that learning from simplicity can enhance safety and target jumping accuracy over trials. Compared to other ILC approaches for legged locomotion, our method can tackle the problem of a long flight phase where control input is not available. In addition, our approach allows the robot to apply what it learns from a simple jumping task to accomplish more challenging tasks within a few trials directly in hardware, instead of learning from scratch. We validate the method via extensive experiments in the A1 model and hardware for various jumping tasks. Starting from a small jump (e.g., a forward leap of 40cm), our learning approach empowers the robot to accomplish a variety of challenging targets, including jumping onto a 20cm high box, jumping to a greater distance of up to 60cm, as well as performing jumps while carrying an unknown payload of 2kg. Our framework can allow the robot to reach the desired position and orientation targets with approximate errors of 1cm and 1 degree within a few trials.