Awesome GitHub RepositoriesNonlinear Optimization Solvers

PythonRobotics 是一个综合性的模块化机器人算法和教育模拟集合，专为自主导航、状态估计和运动控制而设计。该项目提供了一个包含路径规划、定位、建图和运动学的独立实现库，为研究人员和学生实验基础及高级机器人理论提供了资源。 该项目的特色在于以算法为中心的设计，每个模块都作为独立的脚本运行，允许进行独立测试和清晰的教学演示。每个实现都明确映射到学术文献或基础机器人教科书，确保数学模型和控制策略保持可验证性和准确性。用户可以在一个解耦的模拟环境中执行这些场景，该环境维护其内部状态和控制循环，无需外部依赖。 其功能涵盖了广泛的机器人领域，包括空中导航、双足运动和多关节手臂控制。它具有用于概率传感器融合、环境建图和轨迹跟踪的广泛工具包，所有这些都由高性能数值计算驱动。实时几何动画和状态估计直接使用标准绘图库从模拟数据中渲染。

go-datastructures is a collection of thread-safe and lock-free data structures designed for high-performance concurrent applications in Go. It provides a modular library of specialized algorithmic toolsets, including a lock-free collection library and an immutable data structure library. The project distinguishes itself through a suite of persistent AVL trees and hash array mapped tries that use branch-copying to preserve previous versions. It also implements non-blocking hash maps, queues, and tries that enable linearizable snapshots and concurrent updates without the use of mutual exclusion

CVXPY is a Python-embedded domain-specific language for modeling and solving convex optimization problems using natural mathematical syntax. It is built on a disciplined convex programming framework that automatically enforces convexity rules, ensuring that problems formulated by the user are valid for convex solvers. The project also functions as a multi-solver optimization interface, abstracting away backend details and dispatching problems to specialized solvers like ECOS, SCS, and Gurobi without manual configuration. Beyond standard convex optimization, CVXPY extends its reach to geometri

Ceres Solver 是一个 C++ 数值优化库，专注于非线性最小二乘法和无约束优化问题。它作为一个自动微分和鲁棒曲线拟合框架，提供了求解大规模数学模型的工具。 该库以其光束法平差 (bundle adjustment) 能力而著称，利用稀疏矩阵结构来优化 3D 场景点和相机参数。它利用双数自动微分来计算代价函数的导数，无需手动推导雅可比矩阵。 该项目涵盖了广泛的优化功能，包括非欧几里得空间的流形约束、用于减轻异常值的鲁棒损失函数，以及稠密和稀疏线性系统求解。它还提供了用于旋转表示转换、表格数据插值和参数协方差估计的实用工具。 提供针对 Android 和 iOS 目标的构建配置，以支持移动硬件优化。

Drake is a robotics simulation framework and control system modeling tool used for designing, simulating, and verifying the dynamics of complex robotic systems. It functions as a multibody dynamics simulator and a mathematical optimization library, providing a suite of algorithms for trajectory optimization and the simulation of articulated robots. The framework is distinguished by its block-diagram system for composing dynamical subsystems and its ability to formulate and solve diverse mathematical programs, including linear, quadratic, and nonconvex nonlinear problems. It supports specializ

DifferentialEquations.jl is a comprehensive numerical library designed for solving ordinary, stochastic, delay, and algebraic differential equations. It functions as a high-performance solver suite that integrates scientific machine learning, probabilistic programming, and automated differentiation into a unified framework. By leveraging multiple dispatch and symbolic-numeric integration, the library provides a flexible environment for complex mathematical modeling and simulation. The project distinguishes itself through its ability to bridge traditional numerical analysis with modern machine

mujoco_menagerie is a curated library of physical robot specifications and XML model definitions designed for standardized dynamics and contact simulation. It provides a collection of high-quality robot model files for humanoids, quadrupeds, and manipulators, alongside detailed kinematic and inertial parameters used to reproduce real-world robot behavior in virtual environments. The project serves as a repository of robotics simulation assets and MJCF model definitions optimized for accuracy. It includes standardized model libraries specifically for bipedal, quadrupedal, and humanoid hardware

Symbolics.jl is a foundational framework for symbolic mathematics, automated differentiation, and scientific compilation within the Julia programming language. It provides a comprehensive system for algebraic manipulation, expression simplification, and the construction of mathematical models, enabling users to represent complex physical and chemical systems as symbolic equations. The library distinguishes itself through a source-to-source compilation engine that translates high-level symbolic representations directly into optimized, parallelized, and hardware-specific numerical code. By util