Switching control of underactuated multi-channel systems with input constraints for cooperative manipulation

TL;DR

The paper tackles the challenge of coordinating multiple underactuated agents to manipulate a common object under input-direction and magnitude constraints. It combines a backstepping-like stabilizing design for a simplified system with a switching MILP controller and a real-time QP stabilizer to ensure Lyapunov decrease, all within an event-triggered framework that reduces computational load. Semi-global exponential stability is established, with extensions to noninstantaneous switching and quasi-static, nonprehensile manipulation supported by rigorous analysis and validated through 2D/3D simulations. The work demonstrates feasibility and stability guarantees for online channel assignment and control in cooperative manipulation, and shows practical applicability to nonprehensile pushing with real-time computations on standard hardware.

Abstract

This work presents an event-triggered switching control framework for a class of nonlinear underactuated multi-channel systems with input constraints. These systems are inspired by cooperative manipulation tasks involving underactuation, where multiple underactuated agents collaboratively push or pull an object to a target pose. Unlike existing approaches for multi-channel systems, our method addresses underactuation and the potential loss of controllability by additionally addressing channel assignment of agents. To simultaneously account for channel assignment, input constraints, and stabilization, we formulate the control problem as a Mixed Integer Linear Programming and derive sufficient conditions for its feasibility. To improve real-time computation efficiency, we introduce an event-triggered control scheme that maintains stability even between switching events through a quadratic programming-based stabilizing controller. We theoretically establish the semi-global exponential stability of the proposed method and the asymptotic stability of its extension to nonprehensile cooperative manipulation under noninstantaneous switching. The proposed framework is further validated through numerical simulations on 2D and 3D free-flyer systems and multi-robot nonprehensile pushing tasks.

Figures (9)

• Figure 1: Two agents performing cooperative manipulation of a planar object (left) and a spatial object (right). The transparency of agents indicates the agents' pose before contact switching, and the red line is for the force exerted to the object.
• Figure 2: Flow chart of the overall control law.
• Figure 3: Input channel configuration of examples used in simulation (left: square object with $8$ input channels, right: cubic object with $24$ input channels). The rest $12$ input channels not displayed in the cubic object are defined in a symmetric manner.
• Figure 4: A composite image of simulation for Example 1 (square object) with $n_a = 1$.
• Figure 5: Example 1 -- square object with $n_a = 1$ and $u_u = 3 \ N$. The top two rows show the time evolution of the state errors, while the third row presents the Lyapunov function which always remains smaller than $V_d(t) = e^{-c_d t} V_0$, as analyzed in Theorem \ref{['theorem: stability']}. The fourth and fifth rows illustrate the control inputs, where $\delta_{num}(t) = \texttt{diag}(\delta (t)) v_{n_a}$ for $v_{n} = [1;2;\cdots;n] \in \mathbb{R}^n$. Finally, the bottom row displays the auxiliary variable $\rho$ in (\ref{['eq: switching controller']}) on a logarithmic scale, showing $\rho > 0$ if $V > 0$, as analyzed in Theorem \ref{['theorem - feasibility']}.

Theorems & Definitions (29)

• Definition 1: positive spanregis2016properties
• Lemma 1
• proof
• Theorem 1
• proof
• Remark 1
• Claim 1
• proof
• Theorem 2
• proof