two-point-interpolation 0.1.1

Two-point interpolation with constant acceleration and constant jerk

Two Points Interpolation Python

Calculate optimal trajectory (position, velocity, acceleration) between two points with kinematic constraints.

Overview

This library provides two trajectory planning algorithms:

1. Constant Acceleration: Generates smooth trajectories with acceleration limits
2. Constant Jerk: Generates even smoother trajectories with jerk (acceleration derivative) limits

Installation

From PyPI (when published)

pip install two-point-interpolation

From Source

git clone https://github.com/yuokamoto/two_points_interpolation_py.git
cd two_points_interpolation_py
pip install -e .

For Development

git clone https://github.com/yuokamoto/two_points_interpolation_py.git
cd two_points_interpolation_py
pip install -e ".[dev]"

Quick Start

Constant Acceleration

from two_point_interpolation import TwoPointInterpolation

# Create interpolator
interp = TwoPointInterpolation()

# Set start, end, and constraints
interp.init(p0=0.0, pe=100.0, acc_max=2.0, vmax=10.0, dec_max=4.0)

# Calculate trajectory
total_time = interp.calc_trajectory()

# Get state at any time
pos, vel, acc = interp.get_point(t=5.0)

Constant Jerk

from two_point_interpolation.constant_jerk import TwoPointInterpolationJerk

interp = TwoPointInterpolationJerk()
interp.init(p0=0.0, pe=100.0, amax=2.0, vmax=10.0, jmax=1.0)

total_time = interp.calc_trajectory()
pos, vel, acc, jerk = interp.get_point(t=5.0)

Note: Constant jerk implementation is currently under review. See TODO section below.

Examples

Run example scripts to see visualizations:

# Basic constant acceleration
python3 examples/example_constant_acc.py

# Constant jerk (smoother)
python3 examples/example_constant_jerk.py

Testing

# Run all tests
python3 -m pytest tests/ -v

Project Structure

two_points_interpolation_py/
├── two_point_interpolation/              # Main package
│   ├── __init__.py                       # Package exports
│   ├── constant_acc.py                   # Acceleration-based planning
│   └── constant_jerk.py                  # Jerk-based planning (TODO: needs review)
├── examples/                             # Example scripts
│   └── images/                           # Generated plots
├── tests/                                # Unit tests 
└── docs/                                 # Documentation
    ├── CONSTANT_ACC_DERIVATION.md        # Mathematical details
    ├── QUADRATIC_COEFFICIENTS_DERIVATION.md  # Quadratic solution derivation
    └── CHANGELOG.md                      # Version history

Example Results

Case 0: vmax not reached

Parameters: t0=1.0, p0=5, pe=15, acc_max=2.0, dec_max=3.0, vmax=10.0, v0=0, ve=0

Trajectory when the peak velocity is below vmax. Shows two phases: acceleration and deceleration.

Case 1: vmax reached

Parameters: t0=0, p0=0, pe=50, acc_max=2.0, dec_max=4.0, vmax=8.0, v0=2.0, ve=1.0

Trajectory when vmax is reached. Shows three phases: acceleration, constant velocity, and deceleration.

Documentation

• Getting Started: This README
• Mathematical Derivation: docs/CONSTANT_ACC_DERIVATION.md
• Detailed Coefficient Derivation: docs/QUADRATIC_COEFFICIENTS_DERIVATION.md
• Change History: docs/CHANGELOG.md

TODO

Constant Jerk Implementation Issues

The constant_jerk module requires significant improvements:

1. API Contract Violation: The ve (final velocity) parameter is accepted in init() but never used in calculations
2. Debug Output: calc_trajectory() prints debug information to stdout (should use logging or be removed)
3. Time Boundary Bug: Case 3 condition uses 4*t1+2*2*t2+t3 instead of correct 4*t1+2*t2+t3, causing phase transition errors
4. Missing Tests: No test coverage for constant jerk functionality
5. Support acc_max != dec_max: Extend to support independent acceleration/deceleration limits

Other

• Add comprehensive test suite for constant_jerk module
• Verify mathematical correctness of jerk-based trajectories

Requirements

• Python 3.6+
• NumPy
• Matplotlib (for examples)

License

This project is licensed under the Apache License 2.0 - see the LICENSE file for details.

This software is provided "AS IS" without warranty of any kind.