Precise path following and trajectory tracking in cable-driven parallel robots through model predictive control with embedded reference dynamics

Cable-driven parallel robots (CDPRs) are widely adopted in advanced manufacturing systems thanks to their large workspace, ease of construction, and low energy requirements. On the other hand, since the positivity of cable tensions must be ensured, their precise operation is not straightforward. An enhanced model predictive control (MPC) scheme is proposed in this paper for precise path following and trajectory tracking of time-varying references in CDPRs, as those usually required in high-performance manufacturing systems. Path following and trajectory tracking are challenging when references have fast dynamics; indeed, standard MPC formulations lead to good path following responses but, usually, bad performances in terms of trajectory tracking due to the presence of a tracking delay. To overcome this negative aspect, the reference dynamics is embedded into the constrained optimization process through an autonomous state-space approach by exploiting the dynamic mode decomposition (DMD) technique. The novel control approach is named MPC with embedded reference dynamics, MPC-ERD. A further novelty is that the operating limits of the motors in terms of torque and speed, described by their characteristic curve, are included into the controller design as time-varying constraints, together with additional cable tension constraints. The effectiveness of MPC-ERD is numerically validated through a cable-suspended parallel robot (CSPR), and the results are compared with those provided by both standard MPC with embedded integrator (i.e., the “velocity-form model”) and classic MPC without embedded integrator, confirming the superiority of MPC-ERD to ensure precise path and trajectory of the end-effector, with negligible delays and errors.