  In this paper, we establish a task-oriented cross-system design framework to
minimize the required packet rate for timely and accurate modeling of a
real-world robotic arm in the Metaverse, where sensing, communication,
prediction, control, and rendering are considered. To optimize a scheduling
policy and prediction horizons, we design a Constraint Proximal Policy
Optimization(C-PPO) algorithm by integrating domain knowledge from relevant
systems into the advanced reinforcement learning algorithm, Proximal Policy
Optimization(PPO). Specifically, the Jacobian matrix for analyzing the motion
of the robotic arm is included in the state of the C-PPO algorithm, and the
Conditional Value-at-Risk(CVaR) of the state-value function characterizing the
long-term modeling error is adopted in the constraint. Besides, the policy is
represented by a two-branch neural network determining the scheduling policy
and the prediction horizons, respectively. To evaluate our algorithm, we build
a prototype including a real-world robotic arm and its digital model in the
Metaverse. The experimental results indicate that domain knowledge helps to
reduce the convergence time and the required packet rate by up to 50%, and the
cross-system design framework outperforms a baseline framework in terms of the
required packet rate and the tail distribution of the modeling error.
