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# PCS Systems (General)
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The general Piecewise Constant Strain (PCS) implementation provides the core modeling framework for continuum soft robots.
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The general Piecewise Constant Strain (PCS) implementation provides the core modeling framework for continuum soft robots, based on the discrete Cosserat approach proposed by Renda et al. (2018).
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## Overview
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This module contains the fundamental PCS implementation that serves as the foundation for more specialized PCS variants. It provides the core mathematical framework for modeling continuum robots using piecewise constant strain assumptions.
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This module contains the fundamental PCS implementation that serves as the foundation for more specialized PCS variants. It provides the core mathematical framework for modeling continuum robots using piecewise constant strain assumptions, following the discrete Cosserat approach for multisection soft manipulator dynamics.
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## API Reference
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## References
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The PCS (Piecewise Constant Strain) model was originally proposed in:
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Renda, F., Boyer, F., Dias, J., & Seneviratne, L. (2018). Discrete cosserat approach for multisection soft manipulator dynamics. *IEEE Transactions on Robotics*, 34(6), 1518-1533.
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# Planar PCS Symbolic Systems
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The symbolic implementation of Planar PCS systems provides pre-computed symbolic expressions for kinematics and dynamics, offering improved computational performance.
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The symbolic implementation of Planar PCS systems provides pre-computed symbolic expressions for kinematics and dynamics, offering improved computational performance. This implementation is based on the discrete Cosserat approach by Renda et al. (2018).
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## Overview
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This module contains symbolic derivations of the PCS model equations, which are pre-computed using SymPy and then implemented in JAX for fast execution. This approach eliminates the need for numerical differentiation during runtime.
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This module contains symbolic derivations of the PCS model equations, based on the discrete Cosserat approach for multisection soft manipulator dynamics (Renda et al., 2018), which are pre-computed using SymPy and then implemented in JAX for fast execution. This approach eliminates the need for numerical differentiation during runtime.
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## API Reference
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## References
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The PCS (Piecewise Constant Strain) model was originally proposed in:
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Renda, F., Boyer, F., Dias, J., & Seneviratne, L. (2018). Discrete cosserat approach for multisection soft manipulator dynamics. *IEEE Transactions on Robotics*, 34(6), 1518-1533.
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# Planar PCS Systems
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The Planar Piecewise Constant Strain (PCS) systems provide implementations for 2D soft continuum robots using the Cosserat rod theory with piecewise constant strain assumptions.
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The planar Piecewise Constant Strain (PCS) systems provide implementations for 2D soft continuum robots using the Cosserat rod theory with piecewise constant strain assumptions, based on the discrete Cosserat approach by Renda et al. (2018).
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## Overview
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The PCS model divides the continuum robot into segments, each with constant strain properties. This approach provides a good balance between computational efficiency and modeling accuracy for soft continuum robots.
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The PCS model divides the continuum robot into segments, each with constant strain properties. This approach, originally proposed by Renda et al. (2018), provides a good balance between computational efficiency and modeling accuracy for soft continuum robots.
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## Main Implementation
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## References
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The PCS (Piecewise Constant Strain) model was originally proposed in:
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Renda, F., Boyer, F., Dias, J., & Seneviratne, L. (2018). Discrete cosserat approach for multisection soft manipulator dynamics. *IEEE Transactions on Robotics*, 34(6), 1518-1533.
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# Pneumatically Actuated Planar PCS
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Pneumatically actuated Planar PCS systems with pressure-based actuation mechanisms.
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Pneumatically actuated Planar PCS systems with pressure-based actuation mechanisms, extending the discrete Cosserat approach by Renda et al. (2018).
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## Overview
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This module extends the planar PCS model to include pneumatic actuation, where the robot is actuated by controlling internal pressure in chambers or bellows. This actuation method is common in soft pneumatic robots.
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This module extends the planar PCS model (based on the discrete Cosserat approach by Renda et al., 2018) to include pneumatic actuation, where the robot is actuated by controlling internal pressure in chambers or bellows. This actuation method is common in soft pneumatic robots.
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## API Reference
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## References
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The PCS (Piecewise Constant Strain) model was originally proposed in:
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Renda, F., Boyer, F., Dias, J., & Seneviratne, L. (2018). Discrete cosserat approach for multisection soft manipulator dynamics. *IEEE Transactions on Robotics*, 34(6), 1518-1533.
Copy file name to clipboardExpand all lines: docs/api/tendon-planar-pcs.md
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# Tendon Actuated Planar PCS
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Tendon actuated Planar PCS systems with cable-driven actuation mechanisms.
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Tendon actuated Planar PCS systems with cable-driven actuation mechanisms, extending the discrete Cosserat approach by Renda et al. (2018).
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## Overview
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This module extends the planar PCS model to include tendon actuation, where the robot is actuated by controlling the tension in cables or tendons. This actuation method provides precise control and is commonly used in cable-driven continuum robots.
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This module extends the planar PCS model (based on the discrete Cosserat approach by Renda et al., 2018) to include tendon actuation, where the robot is actuated by controlling the tension in cables or tendons. This actuation method provides precise control and is commonly used in cable-driven continuum robots.
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## API Reference
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## References
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The PCS (Piecewise Constant Strain) model was originally proposed in:
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Renda, F., Boyer, F., Dias, J., & Seneviratne, L. (2018). Discrete cosserat approach for multisection soft manipulator dynamics. *IEEE Transactions on Robotics*, 34(6), 1518-1533.
-[:fontawesome-solid-graduation-cap: Google Scholar](https://scholar.google.com/citations?user=7RAU5jYAAAAJ&hl=en)
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Cosimo is the Principal Investigator of the Physical Intelligence Lab and leads the research direction of the project.
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## Maintainers
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The project is actively maintained by:
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## Acknowledgments
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This work is supported by the Physical Intelligence (PhI) Lab at TU Delft and benefits from collaborations with researchers worldwide working on soft robotics and continuum mechanics.
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### Theoretical Foundations
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We gratefully acknowledge the foundational contributions of Prof. Federico Renda, Prof. Frederic Boyer, and Dr. Anup Teejo Mathew, along with all other researchers who developed the soft robot strain models (including PCS - Piecewise Constant Strain, GVS - Geometric Variable-Strain, and other approaches) that are implemented in this library. Their pioneering work in continuum mechanics for soft robotics and the development of modeling frameworks has made this JAX implementation possible.
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### Inspiration
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This package was inspired by **SoRoSim**, a MATLAB toolbox for hybrid rigid-soft robots. We acknowledge the pioneering work of the SoRoSim team in making soft robot modeling accessible to the research community.
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**Reference:**
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Mathew, A. T., Hmida, I. B., Armanini, C., Boyer, F., & Renda, F. (2022). Sorosim: A matlab toolbox for hybrid rigid–soft robots based on the geometric variable-strain approach. *IEEE Robotics & Automation Magazine*, 30(3), 106-122.
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