Optimal and adaptive tracking of periodic trajectories for a four-bar linkage

Industrial automatic machines frequently operate under repetitive and periodic motion regimes, where high-frequency operation, accuracy and robustness are essential requirements. In such contexts, optimal control techniques provide a systematic framework for designing periodic trajectories and feedback laws that achieve high performance. However, the solution of optimal control problems strongly depends on the availability of an accurate dynamic model. In practice, the dynamic parameters are rarely perfectly known and modeling uncertainties are typically present. This thesis addresses these challenges in the context of a four-bar linkage mechanism, a widely adopted closed-chain manipulator in industrial applications. A hierarchical control architecture is proposed, integrating a low-level adaptive controller with a high-level optimal trajectory planner and feedback gain optimizer. The low-level controller is based on a classical Lyapunov-based adaptive control scheme to ensure asymptotic tracking of desired trajectories while estimating uncertain dynamic parameters online. At the high level, periodic trajectory planning is formulated as a nonlinear optimal control problem and solved numerically using IPOPT. Moreover, an optimal feedback gain is computed through an LQR-based approach applied to a locally linearized model of the tracking error dynamics to ensure optimal error correction. Both the trajectory and the feedback gain are periodically updated online using the current parameter estimates, coupling optimization and estimation within a multi-time-scale architecture. The effectiveness of the proposed approach is validated through comprehensive simulations implemented in Python using CasADi for symbolic modeling and numerical optimization.