LeTO: Learning Constrained Visuomotor Policy with Differentiable Trajectory Optimization (2401.17500v3)

Abstract: This paper introduces LeTO, a method for learning constrained visuomotor policy with differentiable trajectory optimization. Our approach integrates a differentiable optimization layer into the neural network. By formulating the optimization layer as a trajectory optimization problem, we enable the model to end-to-end generate actions in a safe and constraint-controlled fashion without extra modules. Our method allows for the introduction of constraint information during the training process, thereby balancing the training objectives of satisfying constraints, smoothing the trajectories, and minimizing errors with demonstrations. This ``gray box" method marries optimization-based safety and interpretability with powerful representational abilities of neural networks. We quantitatively evaluate LeTO in simulation and in the real robot. The results demonstrate that LeTO performs well in both simulated and real-world tasks. In addition, it is capable of generating trajectories that are less uncertain, higher quality, and smoother compared to existing imitation learning methods. Therefore, it is shown that LeTO provides a practical example of how to achieve the integration of neural networks with trajectory optimization. We release our code at https://github.com/ZhengtongXu/LeTO.

• The paper introduces a differentiable optimization layer that integrates directly with neural policies to enforce constraints during training.
• It generates safe, smooth actions by embedding trajectory optimization, thereby reducing uncertainty and improving manipulation performance.
• Experimental results in simulation and real-world settings validate high success rates and enhanced trajectory quality compared to traditional methods.

Overview of LeTO: Learning Constrained Visuomotor Policy with Differentiable Trajectory Optimization

The paper presents a novel method called LeTO, aimed at enhancing visuomotor policy learning through the integration of differentiable trajectory optimization into neural network architectures. This methodological approach addresses a significant gap between the representational strength of neural networks and the safety and interpretability provided by optimization-based methods, particularly in the domain of robotic manipulation. The pervasive challenge in imitation learning, which often results in uncertain and non-smooth trajectories, is effectively mitigated by LeTO through constrained action generation.

Core Contributions and Methodology

LeTO's primary innovation is the embedding of a differentiable optimization layer within the policy learning architecture. This layer is modeled as a trajectory optimization problem, allowing the system to generate safe and smooth actions by adhering to specified constraints. The approach is described as "gray box," effectively blending the black-box nature of neural networks with the transparency of optimization constraints.

Key contributions include:

1. Differentiable Optimization Layer: This layer enables the policy to generate actions constrained by parameters during training, ensuring adherence to the path, velocity, and acceleration limits. It requires no additional modules to control the trajectory, providing a seamless end-to-end learning process.
2. Safe and Constraint-Compliant Actions: The policies learned via LeTO naturally incorporate constraints into action generation, enhancing both the safety and smoothness of trajectories.
3. Evaluation: In simulations, LeTO demonstrates a comparable success rate to state-of-the-art imitation learning methods like diffusion policies, with noticeable improvements in trajectory quality. On real-world tasks where constraints are critical, the policy shows enhanced robustness and safety features. This is particularly noteworthy in the absence of catastrophic failures or system instability, a common issue with traditional imitation learning methods.

Experimental Validation

The experiment results indicate that LeTO consistently generates high-quality, smooth trajectories while maintaining a high success rate in both simulated and real-world robotic tasks. The method outperforms others like LSTM-GMM and IBC in both categories, showing less uncertainty in the generated paths and fewer violations of predefined safety constraints.

• Simulation Results: LeTO achieves a success rate on par with diffusion policy but stands out in generating less uncertain and more refined trajectories.
• Real-world Experiments: It effectively handles tasks with critical constraints, demonstrating superior performance compared to state-of-the-art methods under practical conditions.

Implications for AI and Robotics

The integration of differentiable optimization into policy learning opens new avenues for safer deployment of AI in real-world applications, especially where model interpretability is crucial. This development suggests a shift towards methodologies that combine the strengths of model-based and model-free approaches, offering a robust framework for tackling complex manipulation tasks in stochastic environments.

Future Directions: The research paves the way for further exploration into more computationally efficient differentiable solvers. Additionally, it suggests potential integration with reinforcement learning frameworks, which could further enhance adaptive learning capabilities in dynamic environments where real-time constraints must be adhered to without compromising on policy performance.

In conclusion, LeTO provides a significant advancement in combining neural networks with trajectory optimization, providing a pathway for creating visuomotor policies that are both effective and safe, emphasizing the importance of integrating domain knowledge into AI systems through optimized learning frameworks.