Robust Adaptive Time-Varying Control Barrier Function with Application to Robotic Surface Treatment

TL;DR

The paper addresses enforcing time-varying safety constraints under parametric uncertainty and input disturbances by integrating Robust Adaptive CBFs (RaCBFs) with Time-Varying CBFs (TVCBFs) and Input-to-State Safety (ISSf). It introduces Robust adaptive Time-Varying CBFs (RaTVCBFs) and couples them with Set Membership Identification (SMID) to reduce conservatism, yielding a RaTVCBF-QP for safe control. The approach is applied to robotic surface treatment, where the material removal rate (MRR) must stay within bounds despite changing contact conditions and model uncertainties; simulations and real-robot experiments demonstrate adherence to force bounds and quality guarantees. The work provides formal safety guarantees and practical improvements in robustness and efficiency for time-varying constraints in robotic manipulation tasks.

Abstract

Set invariance techniques such as control barrier functions (CBFs) can be used to enforce time-varying constraints such as keeping a safe distance from dynamic objects. However, existing methods for enforcing time-varying constraints often overlook model uncertainties. To address this issue, this paper proposes a CBFs-based robust adaptive controller design endowing time-varying constraints while considering parametric uncertainty and additive disturbances. To this end, we first leverage Robust adaptive Control Barrier Functions (RaCBFs) to handle model uncertainty, along with the concept of Input-to-State Safety (ISSf) to ensure robustness towards input disturbances. Furthermore, to alleviate the inherent conservatism in robustness, we also incorporate a set membership identification scheme. We demonstrate the proposed method on robotic surface treatment that requires time-varying force bounds to ensure uniform quality, in numerical simulation and real robotic setup, showing that the quality is formally guaranteed within an acceptable range.

Figures (5)

• Figure 1: Block diagram of the control system including a robust adaptive time-varying control barrier function with a given time-varying safe set, $\mathcal{S}(t)$. Given an uncertain system with parametric uncertainty and additive disturbances, the safety filter ensures that the system states stay in a robust subset, $\mathcal{S}_{\bm{\theta}\xspace_{\delta}}^{r} \subseteq \mathcal{S}(t)$. Data-driven update method, Set Membership IDentification (SMID) is used to reduce the maximum possible error $||\bm{\tilde{\vartheta}}||$.
• Figure 2: Admissible time-varying force bounds to guarantee the desired MRR range.
• Figure 3: Pipeline of the robotic surface treatment. First, a user defines the desired MRR. Subsequently, in the force reference generator, we estimate contact area between a tool and a given surface and then calculate the desired contact pressure based on the desired MRR. Afterwards, the desired force is obtained from the desired contact pressure by using \ref{['Preston_equation']}. Finally, we can determine force bounds (e.g. $\pm15\%$ of the desired force) that are used as constraints to ensure the desired MRR in the dotted box.
• Figure 4: The simulation results of quality guarantees with noise in the robotic polishing application. The figures show the performances of each CBFs-based controller in the presence of parametric model uncertainty and input disturbances in the system \ref{['contact_system_model']}. (a) shows the current contact forces provided by each controller, including the admissible contact force bounds in dotted lines, and (b) represents $h$ values to check the constraint conditions; $h\geq 0$ satisfies the force bound constraints. (c) finally presents the performances of quality guarantees on each controller in terms of MRR. Note that we initiate the CBFs-based controllers after the contact forces reach the bound set as shown in (a).
• Figure 5: Results of experimental validation in real robotic setup. (a) shows contact force trajectories of each method in the z-direction, and the desired force for the nominal controller is set to being outside of the force bounds on purpose to check if violations occur or not. (b) presents $h$ functions of each controller, and $h\geq 0$ indicates the current force belongs in the bound set. (c) shows the current MRR of each method with guarantees range in pale green. Note that each controller initiates when the contact happens and the current contact forces are in the desired constraint set.

Theorems & Definitions (6)

• Theorem 1: ShishirISSfCBFs2019
• Theorem 2: lopez2020robust
• Definition 1
• Proposition 1
• proof
• Remark 1