Consistency-Driven Dual LSTM Models for Kinematic Control of a Wearable Soft Robotic Arm

1. Problem Statement

The paper addresses two primary challenges in controlling pneumatically actuated soft robotic arms, particularly for wearable applications:

• Nonlinear Hysteresis: Soft pneumatic actuators (specifically McKibben muscles) exhibit significant hysteresis due to material viscoelasticity, friction, and pneumatic dynamics. The relationship between pressure and length is history-dependent, creating a non-bijective mapping where a single pressure value can correspond to multiple lengths depending on whether the actuator is loading or unloading.
• One-to-Many Mapping (Inverse Kinematics): Unlike rigid robots, soft arms have more degrees of freedom than input actuators. This results in a "one-to-many" problem where a single target end-effector position can be achieved by multiple distinct actuation sequences. Standard supervised learning often fails here, tending to predict a "conditional mean" solution that is physically invalid (i.e., the predicted pressure does not actually result in the target pose when applied).
• Lack of Consistency: Existing machine learning approaches typically train forward (input $\to$ pose) and inverse (pose $\to$ input) models separately. This lack of constraint leads to instability in inverse predictions and a disconnect between the two models.

2. Methodology

The authors propose a Consistency-Driven Dual LSTM Framework integrated with a custom wearable hardware design.

A. Hardware Design

• Actuators: The arm uses McKibben pneumatic artificial muscles (elastic silicone tubes in corrugated fabric sleeves) allowing up to 202% extensibility.
• Structure: It consists of two serial segments, each with three parallel actuators (6 DoF total).
• Stabilization: A central Shape Memory Alloy (SMA) wire constrains axial extension, while three peripheral SMA wires limit torsion.
• Wearability: The device is mounted on the user's forearm via 3D-printed brackets and elastic straps, controlled by proportional valves.

B. Data Collection

• A randomized sequential data collection strategy was used to generate a dataset of 13,000 frames.
• Inputs were randomized 6-dimensional pressure vectors (0–250 kPa) with fixed-sum constraints.
• Data was collected at a quasi-static rate (1 frame/3 seconds) using a motion capture system to record end-effector poses.

C. Model Architecture

The framework employs two distinct Long Short-Term Memory (LSTM) networks:

1. Forward Model:
   • Input: Historical pressure values and their variations (differential terms) from the past two time steps.
   • Output: Predicted end-effector pose.
   • Structure: 2-layer LSTM $\to$ FC-ReLU $\to$ FC-Sigmoid.
2. Inverse Model:
   • Input: Target position increments (current, historical, and repeated future targets) and current pressure sequences.
   • Output: Required driving pressures.
   • Innovation: A "task prior" is incorporated by mapping the target pose into the LSTM's hidden state initialization to guide the sequence learning.

D. Cycle Consistency Loss

To solve the one-to-many ambiguity and ensure physical feasibility, the authors introduce a Cycle Consistency Loss.

• Mechanism: The output of the Inverse Model (predicted pressure) is fed back into the Forward Model to predict the resulting pose.
• Objective: The system minimizes the error between this "re-predicted" pose and the original target pose.
• Formula: $L_{total} = L_{forward} + L_{inverse} + \lambda \cdot L_{consistency}$
• Effect: This penalizes "averaged" solutions that are mathematically correct in regression but physically impossible, forcing the inverse model to select control inputs that are executable under the true forward dynamics.

3. Key Contributions

1. Dual LSTM with Consistency: A novel framework that jointly trains forward and inverse kinematic models using a cycle consistency loss, specifically designed to handle the hysteresis and non-bijective nature of soft actuators.
2. Physical Realism: The consistency loss ensures that inverse predictions are not just statistical averages but physically valid control sequences that can actually achieve the desired pose.
3. Wearable Integration: The development of a functional, forearm-mounted soft robotic arm capable of complex manipulation in confined spaces, moving beyond rehabilitation to "supernumerary" assistance (acting as a "third hand").
4. Task Prior Initialization: A specific architectural modification where target pose information is embedded into the LSTM hidden states to improve convergence and guidance in the inverse model.

4. Results

• Trajectory Tracking: The system successfully tracked four distinct planar trajectories (circle, U-shape, figure-8, star).
  • Average Tracking Error: 31.43 mm.
  • Maximum Error: 65.86 mm.
• Ablation Study: The study compared different loss combinations.
  • Best Performance: The model trained with Forward + Consistency Loss (excluding the direct Inverse Loss) achieved the lowest Mean Error (30.47 mm) and lowest Standard Deviation (14.42 mm).
  • Comparison: This was a significant improvement over the Forward + Inverse + Consistency model (36.03 mm) and the Forward + Inverse model without consistency (43.94 mm).
  • Finding: The direct inverse loss was found to negatively impact training stability, whereas the consistency loss effectively constrained the solution space.
• Wearable Demonstrations: The device successfully performed complex tasks including:
  • Object handover to a human.
  • Pick-and-place around obstacles.
  • Opening drawers and retrieving objects from narrow gaps/pipes.
  • Passing objects through slits and vertical bars.

5. Significance and Impact

• Solving Hysteresis: The approach effectively captures the temporal dependencies and hysteresis loops inherent in soft materials without requiring complex analytical physics models.
• Human-Robot Collaboration: By functioning as a wearable assistive device, it demonstrates the potential for soft robots to act as "third hands" for individuals with impaired hand function, offering high compliance and adaptability in daily life.
• Computational Efficiency: The model's compact structure (LSTMs with small hidden sizes) allows for onboard computation on wearable devices with limited resources, a critical factor for real-world deployment.
• Generalizability: The consistency-driven framework is applicable to various configurations of pneumatically actuated soft robots, offering a general solution to the inverse kinematics problem in soft robotics.