The paper presents the application of artificial intelligence tools for the path planning of complex multi-agent robotic systems. In particular, a solution is proposed to the planning problem for the conjoint operation of two or more mobile robotic fixtures used for the manufacturing of large workpieces, like those used in the aerospace industry. Such fixturing systems have been recently designed and tested, raising hopes to better satisfy the dynamic conditions of modern manufacturing, with its increasing emphasis on flexibility, adaptability, and automation. The proposed planning method is novel in two fundamental aspects. First, it interprets planning as a constraint satisfaction problem (CSP), rather than as a constrained optimisation, an approach ubiquitous in the path and motion planning literature. Secondly, the formulated CSP is solved by a hierarchy of incremental state space search algorithms which differ in some way from the existing state of the art. This hierarchy includes levels related to the robot and workpiece arrangement parameters and to three components of mobile fixture agents: a supporting head, a mobile base, and a parallel manipulator, respectively. Due to the use of CSP search, the planner constitutes a largely application-independent framework, on the basis of which specific industrial implementations can be defined by supplying the relevant physical, geometrical, and time-related constraints.