The rapid advancement of artificial intelligence is enabling the development of increasingly autonomous robots capable of operating beyond engineered factory settings and into the unstructured environments of human life. This shift raises a critical autonomy-alignment problem: how to ensure that a robot's autonomous learning focuses on acquiring knowledge and behaviours that serve human practical objectives while remaining aligned with broader human values (e.g., safety and ethics). This problem remains largely underexplored and lacks a unifying conceptual and formal framework. Here, we address one of its most challenging instances of the problem: open-ended learning (OEL) robots, which autonomously acquire new knowledge and skills through interaction with the environment, guided by intrinsic motivations and self-generated goals. We propose a computational framework, introduced qualitatively and then formalised, to guide the design of OEL architectures that balance autonomy with human control. At its core is the novel concept of purpose, which specifies what humans (designers or users) want the robot to learn, do, or avoid, independently of specific task domains. The framework decomposes the autonomy-alignment problem into four tractable sub-problems: the alignment of robot purposes (hardwired or learnt) with human purposes; the arbitration between multiple purposes; the grounding of abstract purposes into domain-specific goals; and the acquisition of competence to achieve those goals. The framework supports formal definitions of alignment across multiple cases and proofs of necessary and sufficient conditions under which alignment holds. Illustrative hypothetical scenarios showcase the applicability of the framework for guiding the development of purpose-aligned autonomous robots.