Benefiting from the fusion of communication and intelligent technologies, network-enabled robots have become important to support future machine-assisted and unmanned applications. To provide high-quality services for robots in wide areas, hybrid satellite-terrestrial networks are a key technology. Through hybrid networks, computation-intensive and latency-sensitive tasks can be offloaded to mobile edge computing (MEC) servers. However, due to the mobility of mobile robots and unreliable wireless network environments, excessive local computations and frequent service migrations may significantly increase the service delay. To address this issue, this paper aims to minimize the average task completion time for MEC-based offloading initiated by satellite-terrestrial-network-enabled robots. Different from conventional mobility-aware schemes, the proposed scheme makes the offloading decision by jointly considering the mobility control of robots. A joint optimization problem of task offloading and velocity control is formulated. Using Lyapunov optimization, the original optimization is decomposed into a velocity control subproblem and a task offloading subproblem. Then, based on the Markov decision process (MDP), a dual-agent reinforcement learning (RL) algorithm is proposed. The convergence and complexity of the improved RL algorithm are theoretically analyzed, and the simulation results show that the proposed scheme can effectively reduce the offloading delay.