Aerial GRIPPER: A Gradient-based Real-time Inverse-game Predictor and Planner

Zeshuai Chen; Meng Wang; Jindou Jia; Xiang Yu; Lei Guo

cs.ROSep 28, 2026

Aerial GRIPPER: A Gradient-based Real-time Inverse-game Predictor and Planner

Authors: Zeshuai Chen, Meng Wang, Jindou Jia, Xiang Yu, Lei Guo

Organizations: School of Automation Science and Electrical Engineering, Beihang University, 100191, Beijing, China · School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798, Singapore

Abstract

Accurate capture of non-cooperative targets is critical. In an attempt to tackle this intractable challenge, an aerial gripper system integrated with a Gradient-based Real-time Inverse-game Predictor and PlannER (GRIPPER) framework is proposed. The interaction is formulated as a general-sum pursuit-evasion game under incomplete information. Specifically, underlying cost parameters of the target are inferred online, and the open-loop Nash equilibrium (OLNE) strategy is iteratively refined within a receding-horizon loop. To ensure high-frequency execution, a computationally friendly gradient-based inverse-game solver is developed. Without explicit computation of the Hessian inverse, the optimized solution is updated (> 50 Hz) based on implicit differentiation and fast Hessian-vector products. Meanwhile, an anti-disturbance controller is developed to overcome disturbances of uncertain payload and gripper actuation, enabling precise tracking of the planned trajectory and accurate grasping of the target. Simulations and real-world experiments illustrate the superior computational efficiency and task performance of GRIPPER. The task of capturing and delivering a non-cooperative target is accomplished, highlighting the robustness, adaptability, and real-time performance of the framework in highly adversarial scenarios.

Figures & tables

Fig. 1: A custom-made aerial gripper is used to capture a non-cooperative target. (a) Coordinate definition and mechanical structure of the proposed aerial gripper. (b) Illustration and key snapshots of the non-cooperative target capture task. The experimental video can be found in the attached file.

Parameter	Value
UAV mass	2.30 kg
Gripper mass	0.37 kg
Maximum payload	2.50 kg
Minimum grasping diameter	1.0 cm
Maximum grasping diameter	28.5 cm
Minimum servo angle	0 ∘

TABLE I: Physical parameters of the aerial gripper

Fig. 2: Proposed game-theoretic planning algorithm and control scheme. (a) Framework of GRIPPER. The incomplete information PE game is formulated as a bilevel optimization framework. The lower-level optimization solves for the Nash equilibrium. The upper level optimization focuses on the estimation of unknown cost weights by minimizing the deviation between the actual trajectory and the Nash trajectory of the non-cooperative target. (b) Control diagram of the aerial gripper. A PD controller is adopted for position control, and a geometric controller is adopted for attitude control. Two fixed-time SMOs are employed to compensate for disturbances in the translational and rotational loops, respectively.

Forecast Horizon	$N=10$	$N=15$	$N=20$	$N=25$
Computation Time (ms)	13.78	14.26	19.67	35.84
Prediction Error (mm)	1.36	3.28	8.07	42.53
Capture Time (s)	fail	fail	9.63	11.29

TABLE II: Prediction performance under different forecast horizon

Fig. 3: Comparative simulation results. (a) Pursuit-evasion trajectories of different methods. More red lines that reach the goal position means a lower success rate. (b) Trajectory prediction error. The light blue area indicates the transient stage in which the cost parameters have not been estimated since the construction of initial trajectory data takes time. (c) Parameter estimation error.

Method	Comp. time (ms)	Pred. err. (mm)	Est. err. ( $10^{-3}$ )	Succ. rate	Capt. time (s)	Horizon
Proposed	19.67	8.07	2.07	100%	9.28	20
Baseline I	78.71	2.93	58.47	96%	10.70	20
Baseline II	28.55	7.19	1.59	100%	9.63	20
Baseline III	15.26	11.15	-	58%	12.90	20
Baseline IV	$<$ 1	-	-	0%	-	-

TABLE III: Comparative Simulation Results

Fig. 4: Hardware structure of the experiment system.

Description	Method	$\nu_{e}$	$\sigma_{e}$	$\kappa_{e}$
Test I 260g payload	Proposed	3.49	1.74	12.76
	Baseline	7.61 $\uparrow$ 54%	2.85 $\uparrow$ 39%	16.02 $\uparrow$ 20%
	DO-based	5.35 $\uparrow$ 35%	2.56 $\uparrow$ 32%	15.26 $\uparrow$ 16%
Test I 560g payload	Proposed	3.58	2.46	14.15
	Baseline	8.84 $\uparrow$ 60%	4.91 $\uparrow$ 50%	27.07 $\uparrow$ 48%
	DO-based	7.03 $\uparrow$ 49%	3.71 $\uparrow$ 34%	21.12 $\uparrow$ 33%

TABLE IV: comparison results of three control methods (UNIT:

\mathrm{cm}

)

Fig. 5: Experimental results of the aerial gripper’s control performance. (a) Details of Test I in Section VI-C . (b) Tracking details in the Z-axis direction. The shaded area represents the tracking results after releasing the grasped payload. (c) Disturbance estimation performance of different methods in the Z-axis direction. ’Groundtruth’ denotes the truth disturbance calculated by noise-corrupted acceleration measurements offline only for post-analysis. (d) Tracking errors of the UAV and the end-effector under different payloads. (e) Tracking performance under different methods and different payloads. The color bar indicates the tracking error evaluated by standard Euclidean-distance (Eq. ( 47 )).

Fig. 6: Experimental results of the aerial gripper’s control performance. (a) Details of Test II in Section VI-C . (b) Tracking performance under different methods. (c) Torque disturbance estimation performance of different methods in the yaw direction. The right Y-axis represents the PWM signal of the gripper servo. Gripper opens when PWM = -40% and closes when PWM = 40%. (d) Tracking details in the Z-axis direction. (e) Force disturbance estimation performance of different methods in the Z-axis direction.

Fig. 7: Experimental results of non-cooperative target capture task. (a) The scenario of Experiment II in Section VI-D . (b) Estimation performance of unknown cost weight vector $\lambda_{\mathcal{T}}$ . (c) Key snapshots of the trajectory in non-cooperative target capture task. (d) Trajectory prediction error of the non-cooperative target. The green area indicates the transient stage in which the cost parameters have not been estimated since the construction of initial trajectory data takes time. (e) Trajectory of the target and the aerial gripper.

Description	Parameter	Value
Cost weight vector	$\lambda_{\mathcal{T}}$	$[30,10,1]^{\top}$
	$\lambda_{\mathcal{G}}$	$[100,10,10,1]^{\top}$
Initial guess of $\lambda_{\mathcal{T}}$	$\hat{\lambda}_{\mathcal{T},0}$	$[120,20,5,0.5]^{\top}$
Learning rate	$\alpha$	$0.2\times\mathbf{I}_{3N\times 3N}$
Learning rate	$\beta$	$\mathrm{diag}([4,0.8,0.05,0.001])$

TABLE V: Parameters of GRIPPER

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Prior Evolution and Task Alignment for Aerial Grasping

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Robotic Grasping Aerial Manipulation Robust Trajectory Soft Actor-Critic Evolutionary Optimization Methods Animal Vocalizations

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Aerial grasping is a remarkable capability exhibited by predatory birds, allowing them to capture prey through highly coordinated maneuvers in flight. Inspired by this capability, researchers have developed various formulations to reproduce such maneuvers through trajectory optimization. However, two limitations remain in practice. First, the resulting optimization problem is highly nonconvex and sensitive to initialization, making high-quality solutions difficult to obtain under a limited computational budget. Second, prescribed numerical objectives are human-designed abstractions that describe successful grasping through a limited set of mathematically tractable quantities and may not fully capture what determines task success. We investigate how learning can address these limitations within an analytical planner. Accordingly, a trajectory prior is first learned from optimized motions and then evolved through a CEM-based process that evaluates sampled initializations with the deployed optimizer and retains favorable ones as new supervision. An Execution-Aware Critic learns from contact, lift, and completion outcomes to assess whether the optimized trajectories are likely to succeed in physical execution. Its frozen energy can further serve as a differentiable grasping cost, allowing execution data to directly shape trajectory generation. Simulation and real-world experiments demonstrate improved optimization reliability, trajectory consistency, and grasping performance.

Abstract

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