Jia Pan

Yupu Lu, Shijie Lin, Hao Xu et al.

Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have been applied into a learner-verifier framework to identify satisfiable candidates. However, the learner treats Lyapunov conditions as complex constraints for optimisation, which is hard to achieve global convergence. It is also too complicated to implement these Lyapunov conditions for verification. To improve this framework, we treat Lyapunov conditions as inductive biases and design a neural CLF and a CLF-based controller guided by this knowledge. This design enables a stable optimisation process with limited constraints, and allows end-to-end learning of both the CLF and the controller. Our approach achieves a higher convergence rate and larger region of attraction (ROA) in learning the CLF compared to existing methods among abundant experiment cases. We also thoroughly reveal why the success rate decreases with previous methods during learning.

Yajue Yang, Jia Pan, Pinxin Long et al.

In this paper, we present a minimal torque and time variable trajectory optimization method for autonomous excavator considering the soil-tool interaction. The method formulates the excavation motion generation as a trajectory optimization problem and takes into account geometric, kinematic and dynamics constraints. To generate time-efficient trajectory and improve the overall optimization efficiency, we propose a time variable trajectory optimization mechanism so that the time intervals between the keypoints along the trajectory subject to the optimization. As a result, the method uses few keypoints and reduces the total number of optimization variables. We further introduce a soil-tool interaction force model, which considers the geometric shape of the bucket and the physical properties of the soil. The experimental result on a high fidelity dynamic simulator shows our method can generate feasible trajectories, which satisfy excavation task constraints and are adaptive to different soil conditions.