Complete Roadmap for Path Planning and Navigation in Robotics
1. Structured Learning Path
Phase 1: Mathematical Foundations (4-6 weeks)
Graph Theory
- Graph representation (adjacency matrix, adjacency list)
- Graph traversal algorithms (BFS, DFS)
- Shortest path problems
- Minimum spanning trees
- Graph connectivity and components
Computational Geometry
- Point, line, and polygon representations
- Convex hulls
- Line intersection algorithms
- Polygon triangulation
- Voronoi diagrams and Delaunay triangulation
- Visibility graphs
- Computational complexity in geometry
Probability and Statistics
- Probability distributions (Gaussian, uniform, exponential)
- Bayesian probability
- Random sampling methods
- Monte Carlo methods
- Markov chains and processes
Optimization
- Linear and nonlinear programming
- Gradient-based optimization
- Heuristic search methods
- Constrained optimization
- Multi-objective optimization
Linear Algebra
- Vector operations and transformations
- Matrix operations
- Eigenvalues and eigenvectors
- Coordinate transformations (2D/3D)
Phase 2: Configuration Space and World Representation (4-5 weeks)
Configuration Space (C-Space)
- Definition and properties
- C-space for point robots
- C-space for rigid bodies (SE(2), SE(3))
- C-space obstacles (C-obstacles)
- Forward and inverse obstacles
- Degrees of freedom analysis
Environment Representation
- Occupancy grids and maps
- Quadtrees and octrees
- Probabilistic occupancy maps
- Cost maps and inflation layers
- Multi-resolution representations
- 3D voxel grids
Map Types
- Metric maps
- Topological maps
- Hybrid maps
- Semantic maps
- Dynamic maps
Collision Detection
- Bounding volume hierarchies (AABB, OBB, spheres)
- Gilbert-Johnson-Keerthi (GJK) algorithm
- Separating axis theorem
- Distance computation
- Continuous collision detection
Phase 3: Classical Path Planning Algorithms (6-8 weeks)
Graph Search Algorithms
- Dijkstra's algorithm
- Breadth-First Search (BFS)
- Depth-First Search (DFS)
- Uniform Cost Search
- Bellman-Ford algorithm
Informed Search Algorithms
- A* (A-star) algorithm
- Weighted A*
- Iterative Deepening A* (IDA*)
- Greedy Best-First Search
- Heuristic design (Euclidean, Manhattan, Octile)
A* Variants and Optimizations
- Anytime A*
- ARA* (Anytime Repairing A*)
- D* (Dynamic A*)
- D* Lite
- Field D*
- Theta* (any-angle path planning)
- Jump Point Search (JPS)
Potential Field Methods
- Attractive and repulsive potentials
- Gradient descent navigation
- Local minima problem
- Potential field functions
- Navigation functions
Cell Decomposition
- Exact cell decomposition
- Approximate cell decomposition
- Trapezoidal decomposition
- Boustrophedon decomposition
- Morse decomposition
Roadmap Methods
- Visibility graphs
- Voronoi diagrams
- Silhouette methods
- Probabilistic roadmaps (basic concepts)
Phase 4: Sampling-Based Planning (6-8 weeks)
Probabilistic Roadmaps (PRM)
- Construction phase and query phase
- Sampling strategies
- Connection strategies (k-nearest, radius)
- Lazy PRM
- PRM* (asymptotically optimal)
Rapidly-Exploring Random Trees (RRT)
- Basic RRT algorithm
- RRT-Connect (bidirectional RRT)
- Goal-biased sampling
- Informed RRT*
- RRT* (optimal RRT)
RRT Variants
- Kinodynamic RRT
- RRT with dynamics
- Anytime RRT
- Execution Extended RRT (ERRT)
- Transition-based RRT (T-RRT)
- RRT-Sharp
Advanced Sampling Techniques
- Quasi-random sampling (Halton, Sobol sequences)
- Bridge test sampling
- Gaussian sampling
- Obstacle-based sampling
- Adaptive sampling strategies
Batch Informed Trees
- BIT* (Batch Informed Trees)
- ABIT* (Advanced BIT)
- FMT* (Fast Marching Tree)
- Lower Bound Tree RRT (LBT-RRT)
Phase 5: Trajectory Optimization (5-7 weeks)
Parametric Curve Representation
- Polynomial trajectories
- Bezier curves
- B-splines and NURBS
- Clothoid/Euler spirals
- Dubins paths
- Reeds-Shepp curves
Smoothing and Post-Processing
- Shortcut methods
- Path simplification (Douglas-Peucker)
- Elastic band methods
- Gradient-based smoothing
- B-spline fitting
Optimization-Based Planning
- Trajectory optimization formulation
- Shooting methods (direct and indirect)
- Collocation methods
- Sequential Quadratic Programming (SQP)
- Interior point methods
Kinodynamic Planning
- Differential constraints
- State-space planning
- Velocity and acceleration constraints
- Control-based planning
- Motion primitives
Optimal Control Methods
- Minimum time trajectories
- Minimum energy trajectories
- Pontryagin's minimum principle
- Hamilton-Jacobi-Bellman equation
- Dynamic programming
Phase 6: Navigation for Specific Robot Types (6-8 weeks)
Differential Drive Robots
- Kinematics and dynamics
- Pure pursuit controller
- Stanley controller
- Vector field histograms (VFH)
- Dynamic Window Approach (DWA)
Car-Like Robots (Ackermann Steering)
- Bicycle model
- Kinematic constraints
- Dubins and Reeds-Shepp paths
- Hybrid A* for parking
- Lattice-based planning
Holonomic Robots
- Omnidirectional motion
- Mecanum wheels
- Direct path planning
- Time-optimal trajectories
Aerial Vehicles (UAVs/Drones)
- 3D path planning
- Altitude constraints
- Wind considerations
- Coverage path planning
- Multi-rotor dynamics
Manipulator Path Planning
- Joint space vs. task space
- Cartesian path planning
- Collision checking for links
- Self-collision avoidance
- Constrained motion planning
Legged Robots
- Footstep planning
- Terrain analysis
- Contact planning
- Balance constraints
- Gait patterns
Phase 7: Dynamic and Real-Time Planning (5-7 weeks)
Reactive Navigation
- Velocity obstacles (VO)
- Reciprocal velocity obstacles (RVO)
- Dynamic Window Approach (DWA)
- Timed Elastic Band (TEB)
- Model Predictive Control (MPC) for navigation
Replanning Strategies
- Incremental replanning
- Repair-based methods
- Anytime algorithms
- Real-time adaptive planning
- Receding horizon planning
Moving Obstacles
- Prediction of obstacle motion
- Space-time planning
- Velocity space planning
- Safe interval path planning
- Time-parameterized planning
Multi-Agent Path Finding (MAPF)
- Centralized vs. decentralized planning
- Conflict-Based Search (CBS)
- Priority-based planning
- Velocity obstacles for multiple agents
- Coordination spaces
Phase 8: Localization and SLAM (6-8 weeks)
Localization
- Markov localization
- Kalman Filter localization
- Extended Kalman Filter (EKF)
- Particle Filter (Monte Carlo Localization)
- Adaptive Monte Carlo Localization (AMCL)
Simultaneous Localization and Mapping (SLAM)
- EKF-SLAM
- FastSLAM (particle-based)
- Graph-SLAM
- Pose graph optimization
- Bundle adjustment
Visual SLAM
- Feature-based methods (ORB-SLAM, VINS)
- Direct methods (LSD-SLAM, DSO)
- Visual odometry
- Loop closure detection
- Place recognition
LiDAR-Based SLAM
- ICP (Iterative Closest Point)
- NDT (Normal Distributions Transform)
- LOAM (LiDAR Odometry and Mapping)
- Cartographer
- LIO-SAM
Sensor Fusion
- Multi-sensor integration
- IMU integration
- GPS/GNSS fusion
- Camera-LiDAR fusion
- Sensor calibration
Phase 9: Advanced Topics (8-10 weeks)
Learning-Based Planning
- Neural network path planning
- Deep Reinforcement Learning for navigation
- Imitation learning
- Value iteration networks
- Graph neural networks for planning
Semantic Navigation
- Object-goal navigation
- Language-guided navigation
- Semantic mapping
- Scene understanding
- Vision-language models for navigation
Coverage Path Planning
- Area coverage algorithms
- Sweeping patterns
- Multi-robot coverage
- Online coverage
- 3D coverage (inspection tasks)
Uncertainty-Aware Planning
- Belief space planning
- POMDPs for navigation
- Risk-aware planning
- Chance-constrained planning
- Information-theoretic planning
Exploration and Frontier-Based Planning
- Frontier detection
- Information gain
- Next-best-view planning
- Active SLAM
- Exploration-exploitation trade-off
2. Major Algorithms, Techniques, and Tools
Core Path Planning Algorithms
Graph-Based
- Dijkstra's Algorithm
- A* and variants (Weighted A*, ARA*, AD*)
- D* and D* Lite
- Jump Point Search (JPS)
- Theta* and Lazy Theta*
- Field D*
- LPA* (Lifelong Planning A*)
Sampling-Based
- PRM (Probabilistic Roadmap)
- PRM*
- RRT (Rapidly-exploring Random Tree)
- RRT-Connect
- RRT*
- Informed RRT*
- BIT* (Batch Informed Trees)
- FMT* (Fast Marching Tree)
- SST (Stable Sparse RRT)
Optimization-Based
- CHOMP (Covariant Hamiltonian Optimization for Motion Planning)
- TrajOpt (Trajectory Optimization)
- STOMP (Stochastic Trajectory Optimization)
- GPMP (Gaussian Process Motion Planning)
- iLQR/iLQG for trajectory optimization
- Sequential Convex Programming
Reactive/Local Planning
- Dynamic Window Approach (DWA)
- Timed Elastic Band (TEB)
- Velocity Obstacles (VO)
- Reciprocal Velocity Obstacles (RVO/ORCA)
- Vector Field Histogram (VFH/VFH+)
- Nearness Diagram (ND)
- Curvature Velocity Method
Kinodynamic Planning
- State Space RRT
- Kinodynamic RRT
- Hybrid A*
- LQR-RRT
- SST (Stable Sparse Tree)
- Motion Primitives/Lattice Planning
Multi-Agent Planning
- Conflict-Based Search (CBS)
- Enhanced CBS (ECBS)
- M* (Multi-Agent A*)
- ORCA (Optimal Reciprocal Collision Avoidance)
- Push and Swap
- Token Passing
SLAM Algorithms
2D SLAM
- GMapping (Rao-Blackwellized Particle Filter)
- Hector SLAM (scan matching)
- Karto SLAM (graph-based)
- Cartographer (Google)
- CoreSLAM (lightweight)
3D SLAM
- LOAM (LiDAR Odometry and Mapping)
- LeGO-LOAM
- LIO-SAM (LiDAR-Inertial)
- FAST-LIO
- HDL Graph SLAM
Visual SLAM
- ORB-SLAM2/3
- VINS-Mono/Fusion
- LSD-SLAM
- DSO (Direct Sparse Odometry)
- RTAB-Map (RGB-D SLAM)
- OpenVSLAM
Multi-Sensor SLAM
- MSCKF (Multi-State Constraint Kalman Filter)
- ROVIO (Robust Visual Inertial Odometry)
- Kimera (semantic SLAM)
- ElasticFusion
Software Tools and Libraries
Planning Libraries
- OMPL (Open Motion Planning Library) - comprehensive sampling-based planning
- MoveIt - ROS manipulation and planning
- SBPL (Search-Based Planning Library) - lattice planners
- MRPT (Mobile Robot Programming Toolkit)
- FCL (Flexible Collision Library)
ROS/ROS2 Packages
- Navigation Stack (move_base)
- Nav2 (ROS2 navigation)
- Global Planner (Dijkstra, A*)
- Local Planner (DWA, TEB)
- Costmap2D
- AMCL (localization)
Simulation Environments
- Gazebo
- Stage/Stdr
- CoppeliaSim (V-REP)
- Webots
- PyBullet
- CARLA (autonomous driving)
- AirSim (UAV/car simulation)
- Isaac Sim (NVIDIA)
Mapping Tools
- Cartographer
- SLAM Toolbox
- OctoMap (3D occupancy)
- Elevation Mapping
- GridMap library
Visualization
- RViz/RViz2
- Matplotlib
- Plotly
- Three.js for web visualization
- Open3D (3D visualization)
Programming Languages & Frameworks
- C++ (performance-critical code)
- Python (rapid prototyping, learning)
- ROS/ROS2
- MATLAB/Simulink
- Julia (emerging for robotics)
Path Smoothing Libraries
- Cubic Splines
- CasADi (optimization)
- SciPy (Python optimization)
- IPOPT, SNOPT (nonlinear optimization)
Specialized Tools
- Autonomous Driving: Apollo (Baidu), Autoware, CARLA, LGSVL Simulator, OpenPilot
- Drone Navigation: PX4 (flight stack), ArduPilot, RotorS (Gazebo), AirSim, Flightmare
- Multi-Robot Systems: ROS Multi-Master, Fleet Management Systems, Swarm simulators
3. Cutting-Edge Developments (2023-2025)
Learning-Based Navigation
Foundation Models for Navigation
- Vision-Language-Action models (VLA) for navigation
- Large Language Models (LLMs) for high-level planning
- Vision-Language Navigation (VLN) systems
- Zero-shot navigation with pre-trained models
- Multi-modal navigation systems
Neural Planners
- Value Iteration Networks (VIN)
- Differentiable planning networks
- Graph Neural Networks (GNN) for planning
- Neural Motion Planning (NMP)
- Deep reinforcement learning (PPO, SAC) for navigation
- World models for predictive planning
Imitation and Learning from Demonstration
- Behavioral cloning for navigation
- Inverse reinforcement learning
- Goal-conditioned policies
- Learning from human demonstrations
- Sim-to-real transfer techniques
Semantic and Context-Aware Navigation
Semantic Understanding
- Object-goal navigation ("find the chair")
- Audio-visual navigation
- Scene graph navigation
- Affordance-based planning
- Human-aware navigation (social navigation)
Embodied AI
- Embodied Question Answering
- Vision-and-Language Navigation (VLN)
- Multi-object navigation
- Instruction following
- Interactive exploration
Robust and Safe Navigation
Safety and Verification
- Formal verification of planning algorithms
- Control Barrier Functions (CBF) for navigation
- Reachability analysis
- Hamilton-Jacobi reachability
- Probabilistic safety guarantees
Uncertainty-Aware Methods
- Risk-aware planning
- Distributionally robust planning
- Chance-constrained optimization
- Conformal prediction for safety
Advanced SLAM and Perception
Neural SLAM
- NeRF-based SLAM (Neural Radiance Fields)
- 3D Gaussian Splatting for mapping
- Implicit neural representations
- Deep learning feature descriptors
- End-to-end learned SLAM
Multi-Modal SLAM
- Radar-camera-LiDAR fusion
- Event camera SLAM
- Thermal imaging integration
- 4D radar SLAM
Dynamic Environments
- Dynamic SLAM with moving objects
- Panoptic mapping (stuff + things)
- Temporal mapping
- 4D occupancy mapping
Specialized Applications
Off-Road and Challenging Terrains
- Learned terrain traversability
- Self-supervised learning from experience
- Proprioceptive navigation
- Physics-informed planning
Long-Horizon Planning
- Hierarchical planning with learning
- Task and motion planning (TAMP)
- Symbolic planning integration
- Abstract state spaces
Swarm and Multi-Agent
- Decentralized learning for swarms
- Emergent behaviors
- Large-scale coordination (100+ agents)
- Communication-efficient algorithms
Edge Computing and On-Device
- Efficient neural networks (quantization, pruning)
- Neuromorphic navigation
- Event-based processing
- Real-time optimization on embedded systems
Novel Sensing Modalities
Unconventional Sensors
- mmWave radar for navigation
- Sonar and acoustic navigation
- Magnetic field navigation
- Bio-inspired sensing (whiskers, antennae)
Learned Representations
- Self-supervised feature learning
- Contrastive learning for place recognition
- Metric learning for localization
4. Project Ideas by Level
Beginner Projects (1-3 weeks each)
1. Grid-Based A* Pathfinder
- Implement A* on 2D occupancy grid
- Visualize search process
- Compare different heuristics
- Add diagonal movement
2. Dijkstra vs A* Comparison
- Implement both algorithms
- Benchmark performance
- Visualize nodes explored
- Test on various maps
3. Potential Field Navigation
- Simple attractive/repulsive fields
- Navigate to goal avoiding obstacles
- Identify and handle local minima
- Visualization of field gradients
4. Pure Pursuit Path Tracker
- Implement pure pursuit for car-like robot
- Follow pre-defined path
- Tune look-ahead distance
- Simulate in 2D environment
5. Occupancy Grid Mapping
- Build 2D map from simulated sensors
- Implement probabilistic updates
- Log-odds representation
- Visualize in real-time
6. Dead Reckoning Navigator
- Odometry-based navigation
- Track position errors over time
- Visualize drift
- Compare with ground truth
Intermediate Projects (3-6 weeks each)
7. RRT Path Planner Implementation
- Basic RRT from scratch
- Goal-biased sampling
- RRT-Connect bidirectional search
- Compare performance metrics
8. Probabilistic Roadmap (PRM)
- Build roadmap in 2D/3D space
- Implement sampling strategies
- Connection phase optimization
- Query phase for multiple goals
9. Dynamic Window Approach (DWA)
- Local planning for differential drive
- Velocity space sampling
- Cost function design
- Real-time obstacle avoidance
10. Hybrid A* for Car Parking
- Implement Hybrid A* algorithm
- Include Reeds-Shepp heuristics
- Handle kinematic constraints
- Simulate parallel parking scenario
11. Monte Carlo Localization (MCL)
- Particle filter implementation
- Sensor models (range, bearing)
- Resampling strategies
- Kidnapped robot problem
12. Timed Elastic Band (TEB) Planner
- Implement TEB local planner
- Optimization-based trajectory generation
- Dynamic obstacle avoidance
- Test with various robot models
13. Coverage Path Planning
- Boustrophedon decomposition
- Complete area coverage
- Optimize for minimal turns
- Handle complex shaped areas
14. Jump Point Search on Grid
- Implement JPS algorithm
- Compare with standard A*
- Benchmark on large maps
- Visualize jump points
Advanced Projects (6-10 weeks each)
15. RRT* with Informed Sampling
- Implement asymptotically optimal RRT*
- Add informed set sampling
- Compare convergence rates
- 3D implementation
16. Full 2D SLAM System
- EKF-SLAM or GraphSLAM
- Landmark detection and association
- Loop closure detection
- Real-time mapping and localization
17. Visual Odometry Pipeline
- Feature extraction (ORB, SIFT)
- Feature matching and tracking
- Essential matrix estimation
- Scale estimation with IMU
18. Multi-Robot Path Planning
- Implement CBS or ORCA
- Coordinate multiple agents
- Deadlock detection and resolution
- Scalability testing
19. Trajectory Optimization with CHOMP
- Implement CHOMP algorithm
- Gradient-based optimization
- Collision cost formulation
- Compare with sampling-based methods
20. LiDAR-Based SLAM (2D)
- Scan matching (ICP or NDT)
- Pose graph construction
- Loop closure with scan matching
- Real sensor data processing
21. Semantic Navigation System
- Object detection integration
- Semantic map building
- Goal specification by object class
- Navigate to semantic goals
22. MPC for Path Following
- Model Predictive Control formulation
- Receding horizon planning
- Constraint handling
- Real-time implementation
23. Replanning with D* Lite
- Implement D* Lite algorithm
- Dynamic environment changes
- Incremental replanning
- Compare with repeated A*
24. ROS Navigation Stack Integration
- Configure move_base
- Custom costmap layers
- Custom local/global planners
- Deploy on physical robot
Expert/Research Projects (10+ weeks)
25. Learning-Based Navigation with DRL
- Train RL agent (PPO, SAC) for navigation
- Curriculum learning approach
- Sim-to-real transfer
- Compare with classical methods
26. Visual-Inertial SLAM
- Implement VINS or similar
- Tight sensor fusion
- Initialization procedures
- Real-world testing
27. Multi-Floor 3D Navigation
- 3D path planning across levels
- Elevator/stair navigation
- 3D semantic mapping
- Long-term autonomy
28. Social Navigation in Crowds
- Human trajectory prediction
- Socially-aware cost functions
- Implement Social Force Model
- Real-world deployment
29. Neural Motion Planning
- Train neural network planner
- Value Iteration Networks or similar
- Generalization to new environments
- Comparison with OMPL
30. Autonomous Exploration System
- Frontier-based exploration
- Information-theoretic planning
- Active SLAM
- Complete unknown environment
31. Vision-Language Navigation
- Implement VLN system
- Natural language instruction following
- Vision transformer integration
- Test on ALFRED or similar benchmarks
32. BIT* Implementation and Analysis
- Implement Batch Informed Trees
- Performance analysis
- Comparison with RRT* and FMT*
- High-dimensional spaces
33. NeRF-SLAM
- Neural radiance field mapping
- Real-time reconstruction
- Pose estimation from NeRF
- Dense 3D mapping
34. Cooperative Multi-Agent Coverage
- Distributed coverage algorithm
- Communication protocols
- Voronoi-based partitioning
- Real multi-robot deployment
35. End-to-End Learning for Navigation
- Visuomotor policies
- Direct sensor-to-action mapping
- Dataset collection
- Deployment and safety analysis
36. Manipulation with Mobile Base
- Mobile manipulation planning
- Coordinate arm and base
- Whole-body planning
- Pick and place in clutter
37. Terrain-Aware Planning for Legged Robots
- Footstep planning
- Terrain classification
- Contact planning
- Dynamic locomotion
38. Urban Autonomous Navigation
- HD map integration
- Traffic rule compliance
- Behavior prediction
- Deploy in simulator (CARLA)
39. Uncertainty-Aware Planning with POMDPs
- Belief space planning
- Online POMDP solver
- Information gathering behaviors
- Comparison with deterministic planning
40. Quantum-Inspired Path Planning
- Quantum annealing for optimization
- Hybrid classical-quantum algorithms
- Comparative analysis
- Scalability study
Recommended Learning Strategy
Phase-by-Phase Approach
Months 1-2: Foundations
- Focus on mathematical prerequisites
- Implement basic graph algorithms
- Learn C++ or Python thoroughly
- Get comfortable with ROS basics
Months 3-4: Classical Algorithms
- Implement A* from scratch
- Study grid-based methods
- Build intuition with visualizations
- Complete beginner projects
Months 5-6: Sampling-Based Methods
- Deep dive into RRT family
- Implement PRM and variants
- Understand probabilistic completeness
- Work on intermediate projects
Months 7-8: Real Robot Systems
- Learn ROS navigation stack
- Work with real sensors (LiDAR, cameras)
- Implement localization
- Deploy on hardware
Months 9-10: Advanced Topics
- Study SLAM algorithms
- Trajectory optimization
- Multi-agent systems
- Advanced projects
Months 11-12: Specialization
- Choose focus area (learning, SLAM, multi-agent, etc.)
- Research current literature
- Expert projects
- Contribute to open-source
Essential Resources
Textbooks
- "Planning Algorithms" by Steven LaValle (free online)
- "Probabilistic Robotics" by Thrun, Burgard, Fox
- "Principles of Robot Motion" by Choset et al.
- "Robotics, Vision and Control" by Peter Corke
Online Courses
- Coursera: "Motion Planning for Self-Driving Cars"
- Coursera: "Robotics: Computational Motion Planning"
- MIT OCW: "Underactuated Robotics"
- ETH Zurich: "Autonomous Mobile Robots"
Research Venues
- ICRA, IROS (robotics conferences)
- RSS (Robotics: Science and Systems)
- CoRL (Conference on Robot Learning)
- ArXiv (cs.RO category)
Practice Platforms
- ROS/ROS2 tutorials
- OMPL documentation and demos
- GitHub repositories of SLAM systems
- Robotics competitions
This comprehensive roadmap provides a 12-month learning journey with flexibility to adjust based on your interests and career goals. The key is to balance theory with hands-on implementation throughout your learning process.