vvcm-rs

Rust implementation for kinematics of multi-robot transporting systems with a deformable sheet using the Virtual Variable Cables Model (VVCM).

vvcm-rs is implemented in Rust, but it is not limited to Rust projects. The same VVCM forward-kinematics and simulation library is available to Rust, JavaScript/TypeScript, C++, and Python users through the native Rust API, WebAssembly npm packages, C ABI/C++17 wrapper headers, and Python bindings.

If you plan to modify the codebase, read CONTRIBUTING.md first for workflow, structure, and release expectations.

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Citation

If you use the forward kinematics algorithm, please cite:

@article{ma2026stable,
  title = {Stable Kinematics for Multi-Robot Collaborative Transporting System with a Deformable Sheet},
  author = {Ma, Wenyao and Hu, Jiawei and Li, Jiamao and Yi, Jingang and Xiong, Zhenhua},
  year = 2026,
  journal = {IEEE Transactions on Robotics},
  volume = {42},
  pages = {837-853},
  doi = {10.1109/TRO.2026.3653870}
}

For the original VVCM model, please cite:

@article{hu2022multirobot,
  title = {Multi-Robot Object Transport Motion Planning With a Deformable Sheet},
  author = {Hu, Jiawei and Liu, Wenhang and Zhang, Heng and Yi, Jingang and Xiong, Zhenhua},
  year = 2022,
  journal = {IEEE Robotics and Automation Letters},
  volume = {7},
  number = {4},
  pages = {9350--9357}
}

Features

This package includes vvcm-rs for Rust, JavaScript/TypeScript, Python, and C/C++ users with:

  • A Rust VVCM forward-kinematics API built around Point2, Point3, RobotFormation, SheetShape, and FkSolution values that include taut-cable lambda coefficients.
  • Stable-solution search with taut-cable enumeration, candidate solving, and stable-branch filtering.
  • Velocity-driven and manual simulation wrappers.
  • WebAssembly bindings published to npm as @morningfrog/vvcm-rs and the unscoped mirror vvcm-rs, with hand-written TypeScript declarations.
  • Python bindings published as vvcm-rs / vvcm_rs with typed package metadata.
  • C ABI and C++17 wrapper headers for native consumers.
  • Distribution through crates.io, npm, PyPI, GitHub Releases, and vcpkg overlays.

Module Overview

  • fk: forward kinematics engine state and stable-solution entry point.
  • simulation: velocity-driven simulation wrapper.
  • manual_simulation: wrapper for querying a new stable solution from an externally provided robot formation.
  • types: public domain types used by the Rust API.
  • ffi: C ABI implementation behind the C/C++ headers.
  • wasm: WebAssembly bindings compiled with the wasm feature for npm packages.
  • error: crate error type.

Installation

For source-based installation or local development, read CONTRIBUTING.md first.

Rust

Use the crate from crates.io:

cargo add vvcm-rs

Python

Install the package from PyPI:

python -m pip install vvcm-rs

Prebuilt PyPI wheels are published for CPython 3.10 through 3.14 on Windows x64, Linux x64, and macOS arm64. Python 3.9 and other platforms may fall back to building from the source distribution, which requires a local Rust toolchain and Python build tooling.

JavaScript and TypeScript

Install the WebAssembly package from npm:

npm install @morningfrog/vvcm-rs

The unscoped mirror package is also published for users who prefer the shorter install name:

npm install vvcm-rs

The npm packages target modern bundlers such as Vite, Webpack, and Rollup. They include index.d.ts TypeScript declarations and expose ready-to-use named exports from the package entry point.

C and C++

Install the prebuilt package from the GitHub release archive:

vcpkg install vvcm-rs --overlay-ports=<path-to-unzipped-release>/ports --triplet <platform-triplet>

The prebuilt overlay ships native packages for Windows x64, Linux x64, and macOS arm64. It does not require Rust. Use the triplet that matches your platform, such as x64-windows, x64-linux, or arm64-osx.

If you want to build from the repository source instead, use the repo-local overlay port. That overlay builds the native Rust library with Cargo, so Rust must be installed on the machine running vcpkg. Python is only needed when you build the Python extension feature:

vcpkg install vvcm-rs --overlay-ports=<path-to-vvcm-rs>/vcpkg/ports

Then consume the installed CMake package:

find_package(vvcm-rs CONFIG REQUIRED)
target_link_libraries(app PRIVATE vvcm_rs::vvcm_rs)

Usage

The language-specific snippets below assume installation is already complete. Choose the section that matches your project.

The sample outputs below round floating-point values to three decimals; small platform differences are normal.

Rust Usage

After adding vvcm-rs from crates.io, the Rust API looks like this:

use vvcm_rs::{Point2, RobotFormation, SheetShape, VvcmError, VvcmFk};

fn main() -> Result<(), VvcmError> {
    // Robot formation: each Point2 is a robot node position on the world-coordinate XY plane, in millimeters.
    let formation = RobotFormation::new(vec![
        Point2::new(213.7, 122.7),
        Point2::new(804.6, 37.2),
        Point2::new(904.0, 550.0),
        Point2::new(439.3, 715.9),
    ])?;

    // Unfolded sheet: each Point2 is a vertex in the sheet's local coordinate frame, in millimeters.
    let sheet = SheetShape::new(vec![
        Point2::new(-316.1, -421.9),
        Point2::new(803.4, -384.1),
        Point2::new(746.1, 712.8),
        Point2::new(-367.3, 664.2),
    ])?;

    // Create the FK solver for four robots with a 1000 mm hold height.
    let mut fk = VvcmFk::new(4, 1000.0, sheet)?;

    // Ask the solver to enumerate every candidate equilibrium for this formation.
    let solutions = fk.update_stable_solutions(formation)?;

    // Report the total branch count and the subset that is stable.
    println!("all solutions: {}", solutions.all_count());
    println!("stable solutions: {}", solutions.stable_count());

    // Print each stable branch with object pose, virtual object point, taut cables, and matching lambda values.
    for (index, solution) in solutions.stable().enumerate() {
        let lambda_values = solution
            .lambda_values
            .iter()
            .map(|value| format!("{value:.3}"))
            .collect::<Vec<_>>()
            .join(", ");
        println!(
            "#{index}: Po=({:.3}, {:.3}, {:.3}), Vo=({:.3}, {:.3}), taut={:?}, lambda=[{}]",
            solution.po.x,
            solution.po.y,
            solution.po.z,
            solution.vo.x,
            solution.vo.y,
            solution.taut_cables,
            lambda_values,
        );
    }

    Ok(())
}

Expected output:

all solutions: 3
stable solutions: 2
#0: Po=(568.841, 324.728, 336.736), Vo=(238.633, 125.028), taut=[0, 1, 2], lambda=[0.480, 0.039, 0.481]
#1: Po=(557.919, 341.232, 337.247), Vo=(208.794, 152.532), taut=[0, 2, 3], lambda=[0.493, 0.495, 0.012]

JavaScript and TypeScript Usage

After installing @morningfrog/vvcm-rs or vvcm-rs from npm, import the WebAssembly module and use the same solver concepts as the native APIs. Coordinate inputs accept [x, y] tuples or { x, y } objects.

import { VvcmFk } from "@morningfrog/vvcm-rs";

// Robot formation: each tuple is a robot node position on the world-coordinate XY plane, in millimeters.
const formation = [
  [213.7, 122.7],
  [804.6, 37.2],
  [904.0, 550.0],
  [439.3, 715.9],
] as const;

// Unfolded sheet: each tuple is a vertex in the sheet's local coordinate frame, in millimeters.
const sheet = [
  [-316.1, -421.9],
  [803.4, -384.1],
  [746.1, 712.8],
  [-367.3, 664.2],
] as const;

// Create the FK solver for four robots with a 1000 mm hold height.
const fk = new VvcmFk(4, 1000, sheet);

// Solve all candidate equilibria for the current formation.
const solutions = fk.updateStableSolutions(formation);

// Report the total branch count and the subset that is stable.
console.log(`all solutions: ${solutions.allCount}`);
console.log(`stable solutions: ${solutions.stableCount}`);

// Print each stable branch with object pose, virtual object point, taut cables, and matching lambda values.
solutions.solutions
  .filter((solution) => solution.stable)
  .forEach((solution, index) => {
    const po = solution.po;
    const vo = solution.vo;
    const lambdaValues = solution.lambdaValues.map((value) => value.toFixed(3)).join(", ");
    console.log(
      `#${index}: Po=(${po.x.toFixed(3)}, ${po.y.toFixed(3)}, ${po.z.toFixed(3)}), ` +
        `Vo=(${vo.x.toFixed(3)}, ${vo.y.toFixed(3)}), taut=${JSON.stringify(solution.tautCables)}, ` +
        `lambda=[${lambdaValues}]`,
    );
  });

fk.free();

Expected output:

all solutions: 3
stable solutions: 2
#0: Po=(568.841, 324.728, 336.736), Vo=(238.633, 125.028), taut=[0,1,2], lambda=[0.480, 0.039, 0.481]
#1: Po=(557.919, 341.232, 337.247), Vo=(208.794, 152.532), taut=[0,2,3], lambda=[0.493, 0.495, 0.012]

C++ Usage

After installing the vcpkg package or a release archive, consume the installed CMake package and headers directly. The package exports the raw C ABI in vvcm_rs.h and the C++17 RAII wrapper in vvcm_rs.hpp.

find_package(vvcm-rs CONFIG REQUIRED)
target_link_libraries(app PRIVATE vvcm_rs::vvcm_rs)

#include <vvcm_rs.hpp>

#include <cstddef>
#include <iomanip>
#include <iostream>
#include <vector>

int main() {
    using namespace vvcm_rs;

    // Robot formation: each Point2 is a robot node position on the world-coordinate XY plane, in millimeters.
    const std::vector<Point2> formation = {
        Point2(213.7f, 122.7f),
        Point2(804.6f, 37.2f),
        Point2(904.0f, 550.0f),
        Point2(439.3f, 715.9f),
    };

    // Unfolded sheet: each Point2 is a vertex in the sheet's local coordinate frame, in millimeters.
    const std::vector<Point2> sheet = {
        Point2(-316.1f, -421.9f),
        Point2(803.4f, -384.1f),
        Point2(746.1f, 712.8f),
        Point2(-367.3f, 664.2f),
    };

    // Build the solver for four robots and a 1000 mm hold height.
    VvcmFk fk(4, 1000.0f, sheet);
    // Solve all candidate equilibria for the current formation.
    FkSolutions solutions = fk.update_stable_solutions(formation);

    // Report the total branch count and the subset that is stable.
    std::cout << "all solutions: " << solutions.all_count() << "\n";
    std::cout << "stable solutions: " << solutions.stable_count() << "\n";

    // Print each stable branch with object pose, virtual object point, taut cables, and matching lambda values.
    std::cout << std::fixed << std::setprecision(3);
    const std::vector<FkSolution> stable = solutions.stable();
    for (std::size_t index = 0; index < stable.size(); ++index) {
        const auto &solution = stable[index];
        std::cout << "#" << index << ": Po=("
                  << solution.po.x << ", "
                  << solution.po.y << ", "
                  << solution.po.z << "), Vo=("
                  << solution.vo.x << ", "
                  << solution.vo.y << "), taut=[";
        for (std::size_t taut_index = 0; taut_index < solution.taut_cables.size(); ++taut_index) {
            if (taut_index > 0) {
                std::cout << ", ";
            }
            std::cout << solution.taut_cables[taut_index];
        }
        std::cout << "], lambda=[";
        for (std::size_t lambda_index = 0; lambda_index < solution.lambda_values.size(); ++lambda_index) {
            if (lambda_index > 0) {
                std::cout << ", ";
            }
            std::cout << solution.lambda_values[lambda_index];
        }
        std::cout << "]\n";
    }
}

Expected output:

all solutions: 3
stable solutions: 2
#0: Po=(568.841, 324.728, 336.736), Vo=(238.633, 125.028), taut=[0, 1, 2], lambda=[0.480, 0.039, 0.481]
#1: Po=(557.919, 341.232, 337.247), Vo=(208.794, 152.532), taut=[0, 2, 3], lambda=[0.493, 0.495, 0.012]

Python Usage

After installing vvcm-rs from PyPI, import it as vvcm_rs. Coordinate collections accept Point2 values, ordinary list/tuple rows, or sequence-like two-column arrays such as NumPy N x 2 arrays.

from vvcm_rs import VvcmFk

# Robot formation: each tuple is a robot node position on the world-coordinate XY plane, in millimeters.
formation = [
    (213.7, 122.7),
    (804.6, 37.2),
    (904.0, 550.0),
    (439.3, 715.9),
]
# Unfolded sheet: each tuple is a vertex in the sheet's local coordinate frame, in millimeters.
sheet = [
    (-316.1, -421.9),
    (803.4, -384.1),
    (746.1, 712.8),
    (-367.3, 664.2),
]

# Create the solver for four robots and a 1000 mm hold height.
fk = VvcmFk(4, 1000.0, sheet)
# Solve all candidate equilibria for the current formation.
solutions = fk.update_stable_solutions(formation)

# Report the total branch count and the subset that is stable.
print(f"all solutions: {solutions.all_count()}")
print(f"stable solutions: {solutions.stable_count()}")

# Print each stable branch with object pose, virtual object point, taut cables, and matching lambda values.
for index, solution in enumerate(solutions.stable()):
    lambda_values = ", ".join(f"{value:.3f}" for value in solution.lambda_values)
    print(
        f"#{index}: Po=({solution.po.x:.3f}, {solution.po.y:.3f}, {solution.po.z:.3f}), "
        f"Vo=({solution.vo.x:.3f}, {solution.vo.y:.3f}), taut={solution.taut_cables}, "
        f"lambda=[{lambda_values}]"
    )

Expected output:

all solutions: 3
stable solutions: 2
#0: Po=(568.841, 324.728, 336.736), Vo=(238.633, 125.028), taut=[0, 1, 2], lambda=[0.480, 0.039, 0.481]
#1: Po=(557.919, 341.232, 337.247), Vo=(208.794, 152.532), taut=[0, 2, 3], lambda=[0.493, 0.495, 0.012]

For every returned FkSolution, lambda_values is taut-only: lambda_values[i] corresponds to taut_cables[i]. Slack cables are omitted instead of represented by zero-valued placeholders.

Length units are not encoded in the API. Use one consistent unit for formation coordinates, sheet coordinates, and hold height; VvcmFk normalizes coordinates internally for numerical stability and maps returned object positions and virtual object points back to the original coordinate frames.

Error Handling

Forward-kinematics and simulation solves report failures through each language's normal error channel. Error messages are intended for human diagnostics; branch on Rust enum variants, JavaScript error codes, Python exception classes, or C/C++ error codes when program logic needs to distinguish failure modes.

The snippets below show one simple handling pattern for each language: catch the failure, print the message, and branch on the typed error when you need a specific recovery path.

Rust

match fk.update_stable_solutions(formation) {
    Ok(solutions) => {
        println!("stable solutions: {}", solutions.stable_count());
    }
    Err(vvcm_rs::VvcmError::InfeasibleFormation) => {
        eprintln!("formation is infeasible");
    }
    Err(error) => {
        eprintln!("vvcm-rs solve failed: {error}");
    }
}

The main solve errors in Rust are:

  • VvcmError::DimensionMismatch for input size mismatches during construction or solve setup.
  • VvcmError::InfeasibleFormation when the robot formation cannot be realized by the sheet geometry.
  • VvcmError::NoSolution when no candidate branch can be constructed.
  • VvcmError::NoStableSolution when candidate branches exist but none are stable.
  • VvcmError remains the common error type, so Err(error) still catches any of them and Err(vvcm_rs::VvcmError::InfeasibleFormation) can catch one case specifically.

Python

from vvcm_rs import InfeasibleFormationError, VvcmError

try:
    solutions = fk.update_stable_solutions(formation)
except InfeasibleFormationError as error:
    print(f"formation is infeasible: {error}")
except VvcmError as error:
    print(f"vvcm-rs solve failed: {error}")
else:
    print(f"stable solutions: {solutions.stable_count()}")

The main solve errors in Python are:

  • DimensionMismatchError for input size mismatches during construction or solve setup.
  • InfeasibleFormationError when the robot formation cannot be realized by the sheet geometry.
  • NoSolutionError when no candidate branch can be constructed.
  • NoStableSolutionError when candidate branches exist but none are stable.
  • VvcmError remains the common base class, so except VvcmError as error still catches any of them and except InfeasibleFormationError as error can catch one case specifically.

JavaScript and TypeScript

import { VvcmFk, type VvcmError } from "@morningfrog/vvcm-rs";

function isVvcmError(error: unknown): error is VvcmError {
  return error instanceof Error && error.name === "VvcmError" && "code" in error;
}

try {
  const solutions = fk.updateStableSolutions(formation);
  console.log(`stable solutions: ${solutions.stableCount}`);
} catch (error) {
  if (isVvcmError(error) && error.code === "INFEASIBLE_FORMATION") {
    console.error("formation is infeasible");
  } else {
    console.error("vvcm-rs solve failed:", error);
  }
}

The main solve errors in JavaScript and TypeScript are:

  • DIMENSION_MISMATCH for input size mismatches during construction or solve setup.
  • INFEASIBLE_FORMATION when the robot formation cannot be realized by the sheet geometry.
  • NO_SOLUTION when no candidate branch can be constructed.
  • NO_STABLE_SOLUTION when candidate branches exist but none are stable.
  • INVALID_ARGUMENT when a JavaScript value cannot be parsed as the expected point, formation, or sheet input shape.

C

VvcmRsErrorCode code = vvcm_rs_fk_update_stable_solutions(
    fk,
    formation_points,
    formation_point_count);
if (code != VVCM_RS_ERROR_OK) {
    fprintf(stderr, "vvcm-rs failed: %s\n", vvcm_rs_last_error_message());
    if (code == VVCM_RS_ERROR_INFEASIBLE_FORMATION) {
        fprintf(stderr, "formation is infeasible\n");
    }
}

The main solve errors in C are:

  • VVCM_RS_ERROR_DIMENSION_MISMATCH for input size mismatches during construction or solve setup.
  • VVCM_RS_ERROR_INFEASIBLE_FORMATION when the robot formation cannot be realized by the sheet geometry.
  • VVCM_RS_ERROR_NO_SOLUTION when no candidate branch can be constructed.
  • VVCM_RS_ERROR_NO_STABLE_SOLUTION when candidate branches exist but none are stable.
  • vvcm_rs_last_error_message() returns the human-readable message for the most recent failure on the current thread, while vvcm_rs_error_message(code) returns the generic message for a given code.

C++

try {
    vvcm_rs::FkSolutions solutions = fk.update_stable_solutions(formation);
    std::cout << "stable solutions: " << solutions.stable_count() << "\n";
} catch (const vvcm_rs::Error &error) {
    std::cerr << "vvcm-rs failed: " << error.what()
              << " (code " << error.code() << ")\n";
    if (error.code() == VVCM_RS_ERROR_INFEASIBLE_FORMATION) {
        std::cerr << "formation is infeasible\n";
    }
}

The main solve errors in C++ are:

  • VVCM_RS_ERROR_DIMENSION_MISMATCH for input size mismatches during construction or solve setup.
  • VVCM_RS_ERROR_INFEASIBLE_FORMATION when the robot formation cannot be realized by the sheet geometry.
  • VVCM_RS_ERROR_NO_SOLUTION when no candidate branch can be constructed.
  • VVCM_RS_ERROR_NO_STABLE_SOLUTION when candidate branches exist but none are stable.
  • vvcm_rs::Error keeps the originating code, so catch (const vvcm_rs::Error &error) still handles all failures and error.code() lets you branch on one case specifically.

Project links

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  • Released:
Newer release available (2.0.0)

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Credits

Author: MorningFrog

GitHub Statistics

Data verified by PyPI on Jun 20, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

Apache Software License (Apache-2.0)

Requires

Python >=3.9

Tags

robotics kinematics vvcm deformable-sheet

Classifiers

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2.0.0

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1.3.0 This release

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1.2.0

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1.1.0

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1.0.0

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