cs.ROAug 20, 2026

Learning Highly Dynamic Skills Transition for Quadruped Jumping Through Constrained Space

Authors: Zeren Luo, Jiahui Zhang, Yimin Han, Ji Ma, Minghao Lu, Ioannis Havoutis, Peng Lu

Organizations: Adaptive Robotic Controls Lab (ArcLab), Department of Mechanical Engineering, University of Hong Kong, Hong Kong SAR, China. · Dynamic Robots Systems Group (DRS), Oxford Robotics Institute, Department of Engineering Science, University of Oxford, U.K

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Abstract

Although legged animals are capable of performing explosive motions while traversing confined spaces, replicating this behavior in quadrupedal robots has been a longstanding challenge. Here, we propose a hierarchical reinforcement learning pipeline that empowers the robots to perform aggressive locomotion through constrained obstacles--a narrow gate. The imitation learning technique is used to train the low-level policy, which mimics the behaviors of real animals and forms a set of diverse skills. The high-level controller, having an awareness of the capability of low-level skills and acquiring the gate information via vision-based detection, determines the suitable maneuvers with collision-free trajectories to traverse it dynamically. Notably, we also verify that this framework can be extended to other highly dynamic tasks. This is one of the first works that perform autonomous and agile aerial gate traversal tasks on ground-walking robots, extending the lifelike agility of legged robots to match that of their biological counterparts.

Figures & tables

Figure 1: Legged robots require highly aggressive locomotion skills and perception when they jump through a narrow space that is comparable with their body size.
Figure 2: The schematic of the proposed training methodology. In step 1, a low-level locomotion policy is trained using adversarial RL, which guides the learning agent to track the command velocity as well as imitate the motion primitives. In step 2, the locomotion policy is frozen, and a high-level policy is trained to generate the command velocity at a lower frequency. The high-level module receives visual detection results to identify the gate information. When the command actions provided by the high-level policy change, the low-level policy implicitly generates the corresponding skills accordingly.
TermRatioEquationWeight
Task rtTr^{T}_{t}0.8exp⁡{−4(vxycmd−vxy)2}\exp\{-4(\boldsymbol{v}_{xy}^{cmd}-\boldsymbol{v}_{xy})^{2}\}1.0
exp⁡{−4(ωzcmd−ωz)2}\exp\{-4(\boldsymbol{\omega}^{cmd}_{z}-\boldsymbol{\omega}_{z})^{2}\}0.5
mair⋅∑i=14hifeetm^{air}\cdot\sum{{}_{i=1}^{4}}h^{feet}_{i}2.4
Style rtSr^{S}_{t}0.2max⁡[0,1−0.25(Dψ−1)2]\max\left[0,1-0.25(\mathcal{D}_{\psi}-1)^{2}\right]1.0
Regularization rtR{r}^{R}_{t}0.5∣∣τ∣∣2||\boldsymbol{\tau}||^{2}−1×10−5-1\times 10^{-5}
∣∣at−at−1∣∣2||\boldsymbol{a}_{t}-\boldsymbol{a}_{t-1}||^{2}-0.01
Table 1: Reward terms for training low-level policy. (Feet aerial height: feet heights hifeeth^{feet}_{i} filtered by the mask ensuring all feet are in the air mair:⋂i=14{Fi<1.0N}m^{air}:\bigcap_{i=1}^{4}\{F_{i}<1.0N\} ).
Figure 3: Illustration of the model used in the high-level controller training. The sketch shows the components that determine the relative position of the robot w.r.t the gate.
TermEquationWeight
Center tracking\prescriptIvB⋅d^BG\prescript{I}{}{\boldsymbol{v}_{B}}\cdot\widehat{\boldsymbol{d}}_{BG}2.2
Yaw rectification△φz\triangle\varphi_{z} (Eqn. ( 3 ))0.15
Energy dissipation(τ⋅q˙)2(\boldsymbol{\tau}\cdot\boldsymbol{\dot{q}})^{2}-3 ×\times 10−510^{-5}
Action limitsmax⁡(0,atH−vcmdmax,vcmdmin−atH)\max(0,\boldsymbol{a}^{H}_{t}-\boldsymbol{v}^{max}_{cmd},\boldsymbol{v}^{min}_{cmd}-\boldsymbol{a}^{H}_{t})-8.0
Table 2: Reward terms for training high-level policy
Figure 4: Real-hardware setup: ( A ) (1) Forward-facing Intel D435i depth camera, (2) Intel NUC onboard computer, (3) VICON marker, which all mounted on a Unitree Aliengo weighing 22 kg. ( B ) VICON motion capture (MoCap) system, which provides the robot’s pose information. The hardware tests are all conducted in a 6.0m ×\times 3.0m MoCap venue.
ControllerParametersRange [Min, Max]Unit
Low-levelAdded mass[-2.0, 2.0]Kg
Motor strength[0.9, 1.1]-
Motor latency[0.0, 20.0]ms
Motor offset[-0.02, 0.02]Rad
High-levelGate center xx[1.2, 6.0]m
Gate center yy[-1.8, 1.8]m
Table 3: Randomization range of parameters
Figure 5: ( A ) The snapshots are taken from the real deployment of the proposed pipeline on a real Unitree Aliengo robot. The robot detects the gate size and position via onboard sensing. Then, the controllers determine the suitable skills and switching times that enable robots to jump through the gate. (ii) showcases the special case when taking off on uneven terrain. ( B ) The visualization of the base and foot trajectories in ( A )’s test. The high-level policy fully leverages the low-level control policy capability, guiding the foot end-effectors to dodge the gate edge autonomously.
Figure 6: ( A ) Illustration of the continuously varied skills during the whole traversal process. The marked colors correspond to the time periods in the below profiles. ( B(i) ) Gait. ( B(ii) ) Base velocity. ( B(iii) ) Torque of front and rear thigh motors. ( B(iv) ) Pose of front and rear calf joints.
Figure 7: Hierarchical (A) and End-to-end (B) control architecture used for implementations.
Reward TermE2E-BASEE2E-STYLEHier High-levelHier Low-level
Center tracking√\surd√\surd√\surd×\times
Yaw rectification√\surd√\surd√\surd×\times
Energy dissipation√\surd√\surd√\surd×\times
Command action limits×\times×\times√\surd×\times
Velocity tracking×\times×\times×\times√\surd
Style reward×\times√\surd×\times√\surd
Table 4: Reward settings for the training of different methods
Figure 8: Learning curves of compared algorithms. Because of differences in reward setups between [ 4 ] and ours, we recalculate the task rewards during training and log them for comparison only.
Figure 9: The average collision (Left) and measured positions of the calf joint (Right) during the traversal process.
Figure 10: ConsJump is adaptive to scenarios with varying gate positions. ( A ) The function of takeoff distances lTl_{T} in relation to gate heights hGh_{G} . ( B ) The full base trajectories and the front views are demonstrated. Please refer to the linked video for more tests on gate position adaptability.
Figure 11: The system’s generalization to various complex terrains: traversing the gate on continuous stairs ( A ), continuous gaps ( B ) and slope ( C ). The system’s extension to various tasks: jump over a hurdle ( C ), gap ( E ), and fence with boards arranged vertically in a row ( F , with the front view). The accurate shape information in the real-world tests is accessed via the VICON system.
Figure 12: When the gate moves dynamically, the robot can identify the change and adapt its trajectory accordingly. The velocity command given by the high-level controller during the experiment is presented below.
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