From Instantaneous to Predictive Control: A More Intuitive and Tunable MPC Formulation for Robot Manipulators

TL;DR

The paper tackles the tuning burden of MPC for robot manipulators by introducing a practical nonlinear MPC formulation that preserves per-task time constants through a first-order decay-like term and augments it with a prediction horizon. By defining $\boldsymbol{\varepsilon} = \dot{\mathbf{e}}(\mathbf{x},\mathbf{u}) + \mathbf{K}_e \mathbf{e}(\mathbf{x})$ and constructing a cost $l^{\text{C}}$ that penalizes $\boldsymbol{\varepsilon}$ plus control effort, the method retains intuitive tuning while gaining predictive capability. Through a simple motivating example and a surface-following deployment, horizon length is shown to improve tracking and actuation smoothness, with computation remaining feasible for real-time control. The approach facilitates an easier transition from instantaneous to prediction-based control, offering practical benefits for robotic applications and potential broader applicability beyond robotics.

Abstract

Model predictive control (MPC) has become increasingly popular for the control of robot manipulators due to its improved performance compared to instantaneous control approaches. However, tuning these controllers remains a considerable hurdle. To address this hurdle, we propose a practical MPC formulation which retains the more interpretable tuning parameters of the instantaneous control approach while enhancing the performance through a prediction horizon. The formulation is motivated at hand of a simple example, highlighting the practical tuning challenges associated with typical MPC approaches and showing how the proposed formulation alleviates these challenges. Furthermore, the formulation is validated on a surface-following task, illustrating its applicability to industrially relevant scenarios. Although the research is presented in the context of robot manipulator control, we anticipate that the formulation is more broadly applicable.

Figures (11)

• Figure 1: Scenario where a 3-DOF robot manipulator is controlled to follow a Cartesian trajectory.
• Figure 2: Tracking error $e_1$ for different $\mu$ values using objective function A.
• Figure 3: Tracking error $e_1$ for different horizon lengths $N$ using objective function B.
• Figure 4: Tracking error $e_1$ with the proposed objective function.
• Figure 5: Tracking error $e_1$ with the proposed objective function with constraints.