Containerization and orchestration have become two key requirements in software development best practices. Containerization allows for better resource utilization, platform-independent development, and secure deployment of software. Orchestration automates the deployment, networking, scaling, and availability of containerized workloads and services. While containerization is increasingly being adopted in the robotic community, the use of task orchestration platforms (e.g., Kubernetes) is still an open challenge. The biggest limitation is due to the fact that state-of-the-art orchestrators do not support real-time containers, while advanced robotic software often consists of a mix of heterogeneous tasks (i.e., ROS nodes) with different levels of temporal constraints (i.e., mixed-criticality systems). This work addresses this challenge by presenting RT-Kube, a platform that extends the de-facto reference standard for container orchestration, Kubernetes, to schedule tasks with mixed-criticality requirements. It implements monitoring of tasks and detects missed deadlines for those with real-time constraints. It selects low-priority tasks to be migrated at runtime to different units of the computing cluster to free resources and recover from temporal violations. We present quantitative experimental results on the software implementing the mission of a Robotnik RB-Kairos mobile robot to demonstrate the effectiveness of the proposed approach. The source code is publicly available on GitHub.