The rise of multi-tenant shared warehouses has intensified the need for autonomous, secure, and trustworthy cooperation among robotic agents from various vendors, often managed by different parties. This paper addresses the critical challenge of ensuring reliable operations in such environments where the misbehaviour of robotic agents can disturb normal warehouse operations. We propose a trustworthiness framework leveraging distributed ledger technology (DLT) and introducing a novel lightweight proof of location (PoL) mechanism. This mechanism enables robotic agents to verify task completion both physically and cryptographically without imposing significant computational overhead. Our solution includes an algorithmic trust and reputation management system that continuously monitors and evaluates the behaviour of each robot in real-time, ensuring operational integrity. Unlike traditional methods that require synchronous participation or centralised control, our framework supports asynchronous verification, enhancing efficiency and scalability. Through extensive simulations in a warehouse setting, we demonstrate the framework’s capability to detect and mitigate malicious activities, thereby improving both security and performance in multi-vendor autonomous systems (MVAS). Additionally, a conceptual case study in a city street parking scenario highlights the broader applicability and practical feasibility of our approach.