An Efficient Representation of Whole-body Model Predictive Control for Online Compliant Dual-arm Mobile Manipulation

TL;DR

Bezier-curve parameterization is utilized to represent the optimized collision-free trajectories of two collaborating end-effectors in the first MPC, facilitating fast long-horizon object-oriented motion planning in SE(3) while considering approximated feasibility constraints.

Abstract

Dual-arm mobile manipulators can transport and manipulate large-size objects with simple end-effectors. To interact with dynamic environments with strict safety and compliance requirements, achieving whole-body motion planning online while meeting various hard constraints for such highly redundant mobile manipulators poses a significant challenge. We tackle this challenge by presenting an efficient representation of whole-body motion trajectories within our bilevel model-based predictive control (MPC) framework. We utilize Bézier-curve parameterization to represent the optimized collision-free trajectories of two collaborating end-effectors in the first MPC, facilitating fast long-horizon object-oriented motion planning in SE(3) while considering approximated feasibility constraints. This approach is further applied to parameterize whole-body trajectories in the second MPC for whole-body motion generation with predictive admittance control in a relatively short horizon while satisfying whole-body hard constraints. This representation enables two MPCs with continuous properties, thereby avoiding inaccurate model-state transition and dense decision-variable settings in existing MPCs using the discretization method. It strengthens the online execution of the bilevel MPC framework in high-dimensional space and facilitates the generation of consistent commands for our hybrid position/velocity-controlled robot. The simulation comparisons and real-world experiments demonstrate the efficiency and robustness of this approach in various scenarios for static and dynamic obstacle avoidance, and compliant interaction control with the manipulated object and external disturbances.

Figures (17)

• Figure 1: Dual-arm mobile manipulation while avoiding dynamic obstacles and conducting push-recovery. The experimental video can be accessed at https://youtu.be/CEoeLRtpyHw.
• Figure 2: Bilevel MPC framework of whole-body compliant motion generation using model-based predictive control. MPC-T in the first stage is introduced in Section \ref{['subsec:stage1']} and MPC-W in the second stage is presented in Section \ref{['subsec:stage2']}.
• Figure 3: (a) Robot state trajectory of time $\bm{\epsilon}(t)$. (b) Discretized robot states at sampling time knots $\bm{\epsilon}_{[0 \cdots K]}$ (c) Concept of Bézier-curve transcription. The robot state $\bm{\epsilon}_i$ at $i$'s sampling time knot $\bar{t}_i$ is represented by few control points $\bm{E}$ on a Bézier curve $\bm{B}(\bm{E}, \bar{t}_i)$.
• Figure 4: End-effector frames when two palms are set to be parallel. The red, green, and blue lines denote the $x$, $y$, and $z$ axes, respectively.
• Figure 5: Simulation scenario that involves a static obstacle and specifies the directions in which the robot moves.