PaperlayerView exact revision on arXiv

Source-linked AI summary

Learning-Based Pressure Predictive Control of a Vertebraic Soft Robotic Tail

Wenjian Yang, Nan Huang, Yukang Nie, Fang Chen, Wanchao Chi, Jiansheng Dai, Sicong Liu

arXiv:2609.30479v1cs.RO

TL;DR

Soft-tail control is challenged by complex continuum kinematics, especially for non-static motion and coordination with mobile robots. The paper proposes LSTM-based pressure predictive control using inverse kinematics, forward kinematics, and pressure compensation. Compared with IK-only control, it reports lower trajectory RMSE, and an IK-prediction variant reduces coordinated-motion delay.

  • Problem

    Soft-robot kinematics are difficult to model, and learning-based control had unresolved challenges in non-static motion and coordination with mobile robots.

    Source: §I · pp. 1–2

  • Method

    The LSTM-based PPC combines IK, FK, and pressure-compensation networks, with an IK-prediction variant for coordinated motion.

    Source: A. LSTM-Based Pressure Predictive… · p. 2, Ⅶ. CONCLUSION · p. 11

  • Results

    PPC reduced simulated trajectory RMSE compared with IK-only by 69.6%, while IKP reduced coordinated-motion delay by 60.9%.

    Source: Ⅶ. CONCLUSION · p. 11

  • Takeaways & Limitations

    The coordinated-motion demonstration validates the soft-tail quadruped’s functionality for interaction with the environment.

    Source: Ⅶ. CONCLUSION · p. 11

    Evaluation primarily covers accuracy under no-load and no-disturbance conditions, and pneumatic hardware limited tail speed to 85 mm/s.

    Source: C. Limitation and Future Directions · p. 10

Abstract

from arXiv · show

Soft robots have attracted much attention for their safe human-robot interaction and flexibility, but the typical continuum structure and nonlinear material behavior make the kinematics modelling complex, especially in non-static motions. In this work, we proposed an LSTM-based pressure predictive control (PPC) for the motion control of a vertebraic soft robotic tail and the coordination with a quadruped robot. The PPC consists of an inverse kinematics (IK) model, a forward kinematics (FK) model and a pressure compensation (P-comp) model, and achieves non-static and quasi-static motion control of the tail. Compared with the IK-only model, the average RMSE of the PPC's simulation trajectories reduces by 69.8%, when executing target trajectories. In the coordinated motions of the soft tail quadruped, using a prediction data set to train the PPC enables next-moment action prediction and reduces computation time by 60.9%, which enhances the real-time response of the tail to match the quadruped torso's moving rate. The PPC provides a simple and effective method to model the soft tail for both non-static and quasi-static motion control, and grants the soft tail quadruped with the functionality of interacting with the environment.

I. INTRODUCTION

Soft-tail control faces difficult continuum-robot kinematics and gaps in non-static motion and mobile coordination. The paper introduces LSTM-based pressure predictive control and evaluates its accuracy and quadruped coordination.

I. INTRODUCTION

  • Continuum soft-tail kinematics are difficult to model explicitly, while rigid-tail degrees of freedom, speed, and amplitude are constrained by motor number and load capacity.Rigid structures also raise human-robot interaction safety concerns, and off-center weight can affect stability and complicate control.Source: §I · p. 1
  • Learning-based soft-robot control had been demonstrated for quasi-static motion, but non-static motion and coordination with mobile robots remained challenges.Prior robotic-tail studies largely used rigid or cable-driven structures, while soft-tail integration with mobile platforms remained scarce.Source: §I · p. 2
  • 69.8% lower average trajectory RMSE in simulation and 18.8% lower in experiments were achieved by PPC compared with the IK-only model.The simulation reductions were 69.4% in Y and 69.8% in Z; experimental reductions were 12% in Y and 24% in Z.Source: §I · p. 2
  • PPC combines IK, FK, and pressure-compensation networks to generate corrected pressure sequences for tail motion.The proposed LSTM-based controller is intended for both non-static and quasi-static motion.Source: §I · p. 2, Figure 2 · p. 2

II. MOTION CONTROL FRAMEWORK WITH PPC

The PPC framework predicts actuator pressures, estimates the resulting trajectory, and compensates pressure to reduce trajectory error. Its IK, FK, and compensation networks share an LSTM architecture.

II. MOTION CONTROL FRAMEWORK WITH PPC

  • PPC combines IK, FK, and P-comp models; P-comp addresses the time disparity between air pressure and trajectory caused by pneumatic hysteresis.The framework outputs corrected pressure for execution by the pneumatic controller.Source: A. LSTM-Based Pressure Predictive… · p. 2
  • The PPC maps a tail endpoint trajectory sequence to a 10-channel air-pressure sequence, with sequence length denoted by t.The trajectory is represented by Y and Z position coordinates in the YOZ plane.Source: A. LSTM-Based Pressure Predictive… · p. 3
  • IK predicts pressure from the target trajectory, FK predicts the resulting trajectory, and P-comp uses trajectory error to calculate pressure corrections.The corrected pressures are sent to the pneumatic controller to drive the tail.Source: A. LSTM-Based Pressure Predictive… · p. 3
  • IK, FK, and P-comp use an LSTM architecture with sequence input, LSTM, FC1, dropout, FC2, and regression output layers.The dropout probability is 0.5; the network parameters were selected using Bayesian optimization.Source: A. LSTM-Based Pressure Predictive… · p. 3

B. Pneumatic Controller

The tail combines a vertebra-inspired, flexible structure with pneumatic actuation. Its controller regulates pressure through valves, while the tail is built from six joints arranged in two segments.

B. Pneumatic Controller

  • The pneumatic controller opens or closes positive- and negative-pressure valves according to the difference between current and desired actuator pressure.The tail then reaches the desired state and outputs its trajectory in real time.Source: B. Pneumatic Controller · p. 3

A. Design and Fabrication of the BVSR tail

B. Motion Controller and Sensing System

The tail’s pneumatic and motion-capture system supplies synchronized pressure and endpoint-trajectory data for training, using randomized actuator states to sample its workspace.

B. Motion Controller and Sensing System

  • The pneumatic setup pressurizes and depressurizes 10 channels through solenoid valves, measures channel pressures, and records the tail endpoint with motion-capture cameras.The tail is fixed horizontally during capture, and pressure and endpoint-trajectory records are used for network training.Source: B. Motion Controller and Sensing System · pp. 3–4

C. Data Acquisition

  • Four basic bending states—up/down about Y and left/right about Z—organize the movement patterns; five substates per state and an initial state yield 441 configurations across two segments.The states define chamber inflation, deflation, or no-action conditions.Source: C. Data Acquisition · p. 4, Figure 5 · p. 4
  • Randomized chamber states and pressures were repeated over 18 sets, producing 129,600 data pairs before resampling and 48,000 synchronized pairs at 50 Hz.Fifteen sets were used for training and three for testing; the test set also served as validation.Source: C. Data Acquisition · p. 4
  • The recorded random trajectories covered an approximately 200 mm workspace, and the data were organized as aligned and prediction formats for network training.Figure 5 also depicts the FK, IK, and P-comp training processes and FK/IK verification.Source: C. Data Acquisition · p. 4, Figure 5 · p. 4

D. Network Training

The training process learns FK and IK mappings from pressure and trajectory sequences, then trains P-comp on pressure corrections optimized to reduce trajectory error.

D. Network Training

  • The FK network maps pressure sequences to trajectories, while the IK network maps trajectory inputs to pressure sequences; FK test RMSE averaged 8.8 mm in Y and 7.7 mm in Z, and IK test RMSE was 7.5 kPa.The measured-versus-predicted pressure deviation motivates compensating the IK output with P-comp.Source: D. Network Training · pp. 4–5, Table II · p. 5
  • P-comp training data are generated by optimizing pressure corrections for target trajectories, using trajectory error as input alongside the resulting correction values.The optimization uses pretrained IK and FK models and stops when loss falls below 10^-4 or after 100 epochs.Source: D. Network Training · p. 5
  • The trained FK, IK, and P-comp models together form the PPC.The optimization-derived correction sequence and trajectory error are used to train P-comp.Source: D. Network Training · pp. 5–6

IV. VALIDATION OF THE MOTION CONTROL METHOD

Validation compares PPC with IK-only control in simulation and on the tail, finding lower trajectory error with PPC and confirming the FK model’s use as a simulator.

A. Validation of Forward Kinematics Model

  • The FK trajectory matched the real trajectory during three circular-path trials at 75 mm/s, with average RMSE of (5.2 mm, 6.2 mm) in Y and Z.The target circle had a 60 mm radius, supporting use of FK as a simulator for pressure sequences.Source: A. Validation of Forward Kinematics… · p. 6

B. Validation of PPC

  • PPC and IK-only were compared on circle, hexagon, and square targets at 60–85 mm/s, using FK-generated trajectories in simulation and motion-capture trajectories in experiments.The experimental setup fixed the proximal tail end as a cantilever and executed pressure sequences at 50 Hz.Source: B. Validation of PPC · p. 6, §IV · p. 6, A. Validation of Forward Kinematics… · p. 6
  • Simulation RMSE fell 69.8% (69.4% Y, 69.8% Z), while experimental RMSE fell 18.8% (12% Y, 24% Z), with PPC maximum RMSE of 7.1 mm in both axes.Experimental trajectories showed jitter attributed to valve switching and soft-material hysteresis; RMSE remained higher than in simulation.Source: B. Validation of PPC · p. 6, Table III · p. 6

C. Quasi-static Motion with PPC

The PPC also produces quasi-static polygonal motions despite training on non-static data, while IK-only LSTM outperformed GRU on Y-axis trajectory error across multiple tasks.

C. Quasi-static Motion with PPC

  • Quasi-static PPC motion produced average RMSEs of 12.65 mm for the hexagon and 12 mm for the square; the square results were similar to at 7 mm/s.The tail moved at 12–17 mm/s and paused for one second at each interpolated point; reported square RMSEs of 11.53 mm and 14.05 mm.Source: C. Quasi-static Motion with PPC · pp. 6–7

D. Validation of Network

  • Across multiple trajectory-tracking tasks, the IK-only LSTM model had lower Y-axis RMSE than the GRU version.The architectures were trained and validated on identical tasks and datasets; the comparison informed the algorithm choice for PPC.Source: D. Validation of Network · p. 7, Figure 8 · p. 7

E. Hysteresis Reduction

PPC reduces hysteresis relative to IK-only control, and comparisons report trajectory-accuracy advantages and performance across quasi-static and non-static speeds. The paper also describes applying the tail-control system on a quadruped platform.

E. Hysteresis Reduction

  • 22.27% to 18.97% (horizontal) and 24.89% to 18.71% (vertical) are the hysteresis-rate reductions from IK-only control to PPC.The experiments used reciprocating motions in both directions and averaged data across three cycles.Source: E. Hysteresis Reduction · p. 7

F. Control Strategies Comparison

  • PPC shows advantages in absolute and normalized RMSE over compared methods and maintains satisfactory performance from quasi-static to non-static speeds.The comparison considers physics-based and data-driven control strategies.Source: F. Control Strategies Comparison · pp. 7–8

V. MOTION OF THE SOFT TAIL QUADRUPED ROBOT

  • The study adopts a quadruped robot to investigate coordinated motion between its platform and the soft tail.Source: §V · p. 8

A. Modelling of End-point Position

The paper models the tail endpoint relative to the moving quadruped, then evaluates coordinated control that keeps the endpoint near its target. It also reports reduced computation time using pressure prediction and assesses performance under torso motion.

A. Modelling of End-point Position

  • The model transforms the quadruped’s center-of-mass position and torso rotation to the tail root, then estimates inactive-tail endpoint Q as a rigid cylinder.The tail root is expressed as o2 = T1R1o1, and the endpoint as q = T2o2.Source: A. Modelling of End-point Position · p. 8

B. Coordinated Motion Implementation

  • RMSE values at base angles of 15° and -15° were close to those at 0°, supporting use of horizontal-state training data across torso pitch angles.The same pressure sequence was tested at -15°, 0°, and 15° base angles.Source: B. Coordinated Motion Implementation · p. 8
  • 0.161 s to 0.063 s is the average computation-time reduction, a 60.9% decrease with the prediction-data PPC.Trajectory data arrive at 50 Hz; the IKP model predicts pressure for the next moment before FK and P-comp processing.Source: B. Coordinated Motion Implementation · p. 8, Figure 10 · p. 8

C. Tail End-point Control

  • The counter-movement trajectory q1 is defined as q0 − q, the tail motion needed to keep endpoint Q at its initial position during torso motion.The experiment calculates this compensation on the quadruped platform.Source: C. Tail End-point Control · p. 8
  • As torso twisting speed increases, endpoint Q’s moving range grows; hysteresis and PPC computation time also contribute to delayed responses.The coordinated yaw and pitch tests used sinusoidal torso motion at 2.6°/s over -13° to 13°.Source: C. Tail End-point Control · pp. 8–9
  • 9.3% in Y and 9.7% in Z are the ratios of average RMSE over the virtual workspace during endpoint control.In circular torso motion, Q remained within maximum distances of 50.9 mm in Y and 73.3 mm in Z from the target.Source: C. Tail End-point Control · p. 9

D. Bucket-picking Demonstration

The coordinated soft-tail quadruped demonstrates bucket picking by combining torso pitch with tail motion. The paper also reports PPC control results across motion modes and preliminary potential for interaction from a dynamic base.

D. Bucket-picking Demonstration

A. Interpretation of Key Contributions

B. Comparison with the Soft Robotic Control Strategies

The comparison reports lower trajectory RMSE for PPC than several physics-based and neural-network methods, alongside control across a broad range of motion speeds. It also notes that PPC operates under greater structural and gravitational control complexity.

B. Comparison with the Soft Robotic Control Strategies

C. Limitation and Future Directions

The conclusion reports improved trajectory accuracy, quasi-static control, and faster coordinated response, while identifying unmodeled loads and disturbances, hardware limits, and rudimentary coordination as areas for further work.

C. Limitation and Future Directions

  • Evaluation chiefly covers accuracy under no-load and no-disturbance conditions; load and disturbance compensation remains incomplete, coordination is rudimentary, and pneumatic hardware limits speed to 85 mm/s.Source: C. Limitation and Future Directions · p. 10
  • The authors identify hardware upgrades, better system integration, and consideration of inertial forces and loads across an extended speed range as future work.Source: C. Limitation and Future Directions · p. 10

Ⅶ. CONCLUSION

  • The PPC combines IK, FK, and P-comp LSTM networks trained from one data-acquisition process, with P-comp adjusting pressure to reduce trajectory error.Source: Ⅶ. CONCLUSION · p. 11
  • Simulation PPC trajectories had 69.6% lower average RMSE than IK-only (69.4% in Y and 69.8% in Z); experiments showed an 18% reduction (12% in Y and 24% in Z).Source: Ⅶ. CONCLUSION · p. 11
  • 12.65 mm hexagon and 12 mm square average RMSE supported quasi-static control; LSTM IK-only tracked more accurately than GRU, and P-comp reduced hysteresis in both directions.Source: Ⅶ. CONCLUSION · p. 11
  • Replacing IK with IKP for next-state prediction reduced coordinated-motion delay by 60.9%.Source: Ⅶ. CONCLUSION · p. 11
  • The bucket-picking demonstration used coordinated motion to validate the soft-tail quadruped's functionality.Source: Ⅶ. CONCLUSION · p. 11
Loading 2609.30479v1…