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Control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers. However, the existing results are mostly restricted to continuous-time systems. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have actuator, velocity, and position constraints (i.e., relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this article is twofold. The first contribution is the development of novel, robust control barrier functions that ensure constraint satisfaction for sampled-data systems in the presence of model uncertainty and allows for satisfaction of actuator constraints. The second contribution is the application of the proposed method to the challenging …