Robust Control of a Multi-Axis Shape Memory Alloy-Driven Soft Manipulator

TL;DR

This article demonstrates state tracking control for a soft robot manipulator of this type with a robust feedback control scheme, using a static beam bending model to approximate the soft limb as an LTI system and robustness intended to account for the unmodeled dynamics.

Abstract

Control of soft robotic manipulators remains a challenge for designs with advanced capabilities and novel actuation. Two significant limitations are multi-axis, three-dimensional motion of soft bodies alongside actuator dynamics and constraints, both of which are present in shape-memory-alloy (SMA)-powered soft robots. This article addresses both concerns with a robust feedback control scheme, demonstrating state tracking control for a soft robot manipulator of this type. Our controller uses a static beam bending model to approximate the soft limb as an LTI system, alongside a singular-value-decomposition compensator approach to decouple the multi-axial motion and an anti-windup element for the actuator saturation. We prove stability and verify robustness of our controller, with robustness intended to account for the unmodeled dynamics. Our implementation is verified in hardware tests of a soft SMA-powered limb, showing low tracking error, with promising results for future multi-limbed robots.

Figures (6)

• Figure 1: (a) Image of a robot manipulator tracking a reference bend angle. (b) Labelled image of critical components of the soft robotic manipulator. (c) Schematic of the input coordinates, $u_i$, which are along the axes of diagonal SMA pairs. (d) Schematic of the the output coordinates, $\theta_i$, which are bend angles in the yaw and pitch directions. (e) Simplified block diagram of control structure.
• Figure 2: Nominal controller for our system including a PI block and SVD pre- and post-compensators.
• Figure 3: Block Diagram of the full closed loop system. $A, B, C, D$ refer to the state space matrices of the nominal controller, $BD^{-1}$ is the anti-windup block, $N$ is the nonlinear adjustment to maintain the direction of the commanded input, and the block directly before the plant, $G$, is the nonlinear operator that constrains the inputs delivered to the plant to [-1,1].
• Figure 4: (a) Modified block diagram, replacing the nonlinearities with a cone-bounded uncertainty, $\Delta$. (b) Standard $M\Delta$ interconnection for stability analysis. The block diagram in (a) is put into this form for our analysis. (c) Inclusion of an additional multiplicative $\Delta$ block for unmodeled dynamics.
• Figure 5: Test setup for controller performance evaluation.