Coming soon
Robotics Engineering
From joint angles to a robot that finishes the job.
The complete course
- modules
- 57
- topics
- 598
- min lessons
- 15
58%
of employers expect robots and autonomous systems to transform their business by 2030.
What you'll be able to do.
Solve forward and inverse kinematics
Stage 2 · Spatial Kinematics
Model dynamics, torque and contact forces
Stage 3 · Dynamics & Actuation
Fuse sensors into a reliable state estimate
Stage 4 · Sensing, Estimation & Software
Plan collision-free motion and stable grasps
Stage 5 · Planning & Manipulation
Integrate and commission a working prototype
Stage 6 · Mobile Systems & Verification
Ship a robot task with failure recovery
Stage 7 · Laboratory & Capstone
Seven stages.One steady climb.
Frames and joints, forces and sensors, plans and grasps — then the whole robot.
57modules
in 7 stages
598topics
≈ 10 per module
≈150hours
of 15-minute lessons
≈20months
≈10months
≈5months
to finish the whole course
- 1
Foundations & Math
Requirements and the math you'll use
4 modules · 41 topics · ≈ 10 hr
- 2
Spatial Kinematics
Where every joint and frame sits
11 modules · 115 topics · ≈ 29 hr
- 3
Dynamics & Actuation
Forces, motors and contact
7 modules · 72 topics · ≈ 18 hr
- 4
Sensing, Estimation & Software
What the robot senses and believes
7 modules · 76 topics · ≈ 19 hr
- 5
Planning & Manipulation
Getting there, then picking it up
13 modules · 142 topics · ≈ 36 hr
- 6
Mobile Systems & Verification
Wheels, fleets and proof it works
12 modules · 121 topics · ≈ 30 hr
- 7
Laboratory & Capstone
Your robot, from model to prototype
3 modules · 31 topics · ≈ 8 hr
Months
0481202460123
MonthsFinish · ≈ 20 months · ≈ 10 months · ≈ 5 months
Hours and months are estimates: one 15-minute lesson per topic, every day.
Every module.Every topic.
Stage 1
Foundations & Math
Requirements and the math you'll use
4 modules · 41 topics
1Foundations of Robotics Engineering9 topics
- Robots as Embodied Computational Systems
- Sensing, Decision, Action, and Physical Feedback
- Robot Autonomy and Levels of Task Responsibility
- Manipulation, Mobility, and Physical Interaction
- Robot State, Configuration, Action, and Observation
- Model-Based and Data-Driven Approaches to Robotics
- The Relationship Between Robot Hardware and Algorithms
- Robot Capability, Performance, and Operating Conditions
- The Robotics Engineering Development Lifecycle
2Robot Tasks and Engineering Requirements11 topics
- Translating an Application into a Robot Task
- Defining Task Inputs, Outputs, and Success Conditions
- Describing Objects, Environments, and Disturbances
- Functional and Performance Requirements
- Reach, Payload, Speed, and Precision Requirements
- Duty Cycles and Mission Duration
- Operating Envelopes and Environmental Constraints
- Expected Variability and Exceptional Conditions
- Allocating Error, Timing, and Reliability Budgets
- Requirement Traceability and Acceptance Criteria
- Evaluating Whether a Task Is Physically Feasible
3Robot Architecture and Interface Design10 topics
- Functional Decomposition of a Robotic System
- Mechanical, Electrical, Computational, and Data Interfaces
- Separating Sensing, Estimation, Planning, and Execution
- Centralized and Distributed Robot Architectures
- Hardware Abstraction and Replaceable Components
- Command Ownership and Authority Boundaries
- State Feedback and Component Health Interfaces
- Interface Units, Coordinate Frames, and Conventions
- Startup, Shutdown, and Operating Modes
- Architecture Tradeoffs Across Cost, Capability, and Complexity
4Mathematical and Computational Tools for Robotics11 topics
- Vectors, Bases, and Coordinate Representations
- Matrix Operations in Robot Models
- Linear Systems and Least-Squares Solutions
- Rank, Null Spaces, and Singular Value Decomposition
- Derivatives, Gradients, and Jacobians
- Ordinary Differential Equations and State Evolution
- Numerical Integration and Discretization Error
- Constrained Optimization for Robot Problems
- Probability, Covariance, and Measurement Uncertainty
- Numerical Conditioning, Scaling, and Floating-Point Error
- Units and Dimensional Consistency in Robot Calculations
Stage 2
Spatial Kinematics
Where every joint and frame sits
11 modules · 115 topics
5Robot Mechanisms and Degrees of Freedom10 topics
- Links, Joints, and Kinematic Chains
- Revolute, Prismatic, Helical, and Compound Joints
- Serial, Parallel, and Hybrid Mechanisms
- Joint Coordinates and Independent Motion Variables
- Degrees of Freedom and Mechanism Mobility
- Mobility Counting and Its Assumptions
- Actuated, Passive, and Underactuated Coordinates
- Open Chains, Closed Loops, and Kinematic Trees
- Joint Limits and Mechanical Motion Constraints
- Mechanism Selection from Task Requirements
6Coordinate Frames and Spatial Transformations10 topics
- World, Base, Joint, Tool, Sensor, and Object Frames
- Right-Handed Coordinate Systems and Axis Conventions
- Expressing Points and Vectors in Different Frames
- Active Transformations and Passive Coordinate Changes
- Rotation and Translation as Distinct Operations
- Homogeneous Transformation Matrices
- Transformation Composition and Order Dependence
- Inverting Rigid Transformations
- Frame Trees and Transformation Chains
- Detecting Frame, Sign, and Unit Errors
7Representing Orientation in Three Dimensions11 topics
- Rotation Matrices and Their Constraints
- Euler Angles and Rotation Sequences
- Roll, Pitch, Yaw, and Convention Ambiguities
- Axis-Angle Representations
- Unit Quaternions and Quaternion Composition
- Quaternion Sign Ambiguity and Normalization
- Converting Between Orientation Representations
- Gimbal Lock and Representation Singularities
- Orientation Error and Rotation Distance
- Interpolating Orientations Along a Motion
- Averaging and Comparing Noisy Orientation Estimates
8Rigid-Body Motion and Screw Coordinates9 topics
- The Rotation Group SO(3)
- The Rigid-Motion Group SE(3)
- Skew-Symmetric Matrices and Cross Products
- Angular Velocity in Moving and Fixed Frames
- Twists and Instantaneous Rigid-Body Motion
- Screw Axes, Pitch, and Joint Motion
- Exponential and Logarithmic Maps for Robot Poses
- Adjoint Transformations of Spatial Motion
- Consistent Spatial and Body Coordinate Conventions
9Configuration Spaces and Robot Workspaces10 topics
- Joint Space, Task Space, and Operational Coordinates
- Configuration Space Dimension and Topology
- Periodic Coordinates and Angular Wraparound
- Position Tasks and Full-Pose Tasks
- Reachable and Dexterous Workspaces
- Workspace Boundaries and Internal Exclusions
- Joint Limits as Configuration Constraints
- Holonomic and Nonholonomic Constraints
- Task Constraints as Lower-Dimensional Configuration Sets
- Numerical Workspace Exploration and Visualization
10Forward Kinematics11 topics
- Building a Kinematic Model from a Mechanism
- Planar Manipulator Forward Kinematics
- Spatial Serial-Chain Forward Kinematics
- Assigning Link Frames Consistently
- Standard and Modified Denavit-Hartenberg Conventions
- Product-of-Exponentials Kinematic Models
- Space-Frame and Body-Frame Formulations
- Tool Offsets and Additional Fixed Transforms
- Kinematics of Branched Robot Models
- Evaluating Intermediate Link Poses
- Validating Forward Kinematics Against Geometry and Measurements
11Geometric and Analytical Inverse Kinematics10 topics
- Formulating Position and Orientation Goals
- Geometric Solutions for Planar Arms
- Reachability Tests Before Solving
- Multiple Inverse-Kinematics Solutions
- Elbow, Shoulder, and Wrist Configuration Branches
- Kinematic Decoupling for Suitable Robot Structures
- Joint Limits and Admissible Solutions
- Selecting Solutions Relative to a Starting Configuration
- Maintaining Solution Continuity Along a Path
- Recognizing Structures Without Practical Closed-Form Solutions
12Numerical and Constrained Inverse Kinematics12 topics
- Defining Pose Residuals for Numerical Solvers
- Iterative Linearization of Kinematic Equations
- Newton and Gauss-Newton Solution Strategies
- Pseudoinverse Updates and Damped Least Squares
- Weighting Position and Orientation Errors
- Initial Guesses, Multiple Starts, and Local Minima
- Joint Bounds and Inequality Constraints
- Orientation Cones and Partial-Pose Constraints
- Collision-Aware Inverse Kinematics
- Posture Preferences and Secondary Objectives
- Convergence Criteria and Failure Diagnostics
- Evaluating Solver Robustness Across Target Sets
13Differential Kinematics and Jacobians11 topics
- Mapping Joint Rates to End-Effector Velocity
- Geometric and Analytical Jacobians
- Constructing Jacobians from Joint Axes
- Space Jacobians and Body Jacobians
- Transforming Jacobians Between Frames
- Translational and Rotational Task Jacobians
- Jacobians for Intermediate Links and Contact Points
- Differential Inverse Kinematics
- Joint Acceleration and End-Effector Acceleration
- Jacobian Time Derivatives
- Checking Jacobians with Numerical Differentiation
14Singularities, Redundancy, and Dexterity11 topics
- Kinematic Singularities and Rank Loss
- Workspace-Boundary and Internal Singularities
- Velocity Amplification Near Singular Configurations
- Manipulability Ellipsoids and Their Interpretation
- Task Scaling and Dimensionally Consistent Dexterity Metrics
- Condition Numbers as Configuration Diagnostics
- Redundant Robots and Self-Motion
- Null-Space Motion and Task Preservation
- Joint Centering and Joint-Limit Avoidance
- Task Priorities and Conflicting Objectives
- Planning Motions Through Regions of Poor Dexterity
15Closed-Chain and Parallel Robot Kinematics10 topics
- Loop-Closure Equations
- Independent and Dependent Joint Coordinates
- Forward and Inverse Problems in Parallel Mechanisms
- Assembly Modes and Working Modes
- Constraint Jacobians and Admissible Motion
- Serial and Parallel Singularities
- Workspace Restrictions from Loop Closure
- Kinematics of Mechanically Coupled Arms
- Numerical Solution of Closed-Chain Constraints
- Maintaining Constraint Consistency During Motion
Stage 3
Dynamics & Actuation
Forces, motors and contact
7 modules · 72 topics
16Robot Statics and Force Transmission9 topics
- Forces, Moments, and Spatial Wrenches
- Wrench Transformation Between Coordinate Frames
- Static Equilibrium of Robot Links
- Virtual Work and Generalized Forces
- Mapping End-Effector Wrenches to Joint Torques
- Gravity Loads and Configuration Dependence
- Force Transmission and Mechanical Advantage
- Joint Torque Limits and Feasible Tool Wrenches
- Interpreting Force Capability Near Singularities
17Rigid-Body Dynamics for Robots11 topics
- Mass, Center of Mass, and Inertia Tensors
- Expressing Inertia in Different Coordinate Frames
- The Parallel-Axis Theorem in Robot Models
- Linear and Angular Momentum
- Kinetic and Potential Energy
- Newton-Euler Equations for a Rigid Body
- Generalized Coordinates and the Lagrangian
- Configuration-Dependent Inertia
- Coriolis, Centrifugal, and Gravity Effects
- External Forces and Generalized Joint Loads
- Energy and Momentum Checks for Dynamic Models
18Manipulator Dynamics and Computational Algorithms11 topics
- The Manipulator Equation of Motion
- Deriving Dynamics for a Simple Robot Arm
- Interpreting the Joint-Space Mass Matrix
- Inverse Dynamics and Required Joint Effort
- Recursive Newton-Euler Computation
- Forward Dynamics and Motion Prediction
- Efficient Inertia and Forward-Dynamics Algorithms
- Task-Space Dynamic Relationships
- Dynamics with Kinematic Constraints
- Payload and Tool Contributions to Robot Dynamics
- Comparing Rigid-Body Models with Measured Motion
19Actuation and Joint Capability Models11 topics
- Position, Velocity, Torque, and Effort Interfaces
- Motor-Side and Joint-Side Quantities
- Gear Ratios and Reflected Inertia
- Torque-Speed Envelopes and Power Limits
- Continuous and Peak Joint Ratings
- Transmission Efficiency and Backdrivability
- Joint Friction, Stiction, and Dead Zones
- Backlash and Hysteresis in Robot Motion
- Series Elasticity and Joint Deflection
- Thermal Derating and Duty-Cycle Constraints
- Translating Joint Capabilities into Task Feasibility
20Robot Accuracy, Compliance, and Error Budgets9 topics
- Accuracy, Precision, Repeatability, and Resolution
- Sources of End-Effector Position and Orientation Error
- Propagating Joint Errors Through Kinematics
- Geometric Error and Nongeometric Error
- Link, Joint, and Mounting Compliance
- Cartesian Stiffness and Configuration Dependence
- Payload Deflection and Tool Compliance
- Thermal Drift and Time-Dependent Accuracy
- Allocating and Verifying a Robot Error Budget
21Motion Commands and Tracking Behavior11 topics
- Joint-Space and Cartesian Command Interfaces
- Position Setpoints and Time-Indexed Trajectories
- Velocity Commands and Integrated Motion
- Effort Commands and Gravity Compensation Interfaces
- Feedforward Terms from a Robot Model
- Feedback Tracking in the Robot Execution Chain
- Tracking Error, Lag, Overshoot, and Settling
- Command Saturation and Rate Limits
- Matching Trajectory Demands to Tracking Capability
- Switching Motion Modes Without Command Discontinuities
- Measuring Tracking Performance Under Changing Loads
22Contact Behavior and Force Interfaces10 topics
- Free Motion and Constrained Motion
- Choosing Position, Force, or Compliance Objectives
- Contact Frames and Task Direction Selection
- Direct Force Commands and Force Feedback
- Impedance as a Motion-to-Force Relationship
- Admittance as a Force-to-Motion Relationship
- Selecting Apparent Stiffness and Damping for a Task
- Combining Motion and Force Objectives in Different Directions
- Contact Transitions, Delays, and Unwanted Oscillation
- Evaluating Contact Behavior Against Task Limits
Stage 4
Sensing, Estimation & Software
What the robot senses and believes
7 modules · 76 topics
23Robot Sensing and Measurement Interfaces11 topics
- Proprioceptive and Exteroceptive Measurements
- Joint Position and Velocity Measurements
- Encoders, Index References, and Homing Information
- Torque Sensors and Motor-Current-Based Effort Estimates
- Force-Torque Sensors and Load Measurement
- Inertial Measurements and Their Reference Frames
- Contact, Proximity, and Tactile Signals
- Range and Pose Measurements as Robot Inputs
- Sensor Resolution, Bandwidth, and Latency
- Bias, Drift, Noise, Saturation, and Missing Data
- Measurement Timestamps, Units, and Validity Flags
24Robot State Estimation and Uncertainty11 topics
- Choosing State Variables for a Robot Task
- Process Models and Measurement Models
- Prediction and Measurement Correction
- Propagating State and Measurement Covariance
- Combining Measurements with Different Uncertainties
- Kalman Filtering for Simple Robot State Models
- Local Linearization for Nonlinear Robot Estimation
- Observability and Unmeasured State Components
- Innovation Checks and Outlier Rejection
- Delayed, Intermittent, and Asynchronous Measurements
- Relating Estimation Uncertainty to Motion Decisions
25Robot Calibration and Parameter Identification12 topics
- Calibration Objectives and Reference Measurements
- Joint Zero Offsets and Encoder Scale Factors
- Geometric and Kinematic Parameter Calibration
- Tool Center Point Calibration
- Base-to-World Frame Calibration
- Sensor-to-Robot Extrinsic Calibration
- Hand-Eye Calibration from Robot and Sensor Motions
- Force-Torque Sensor Bias and Tool-Weight Compensation
- Payload Mass and Center-of-Mass Identification
- Identifying Friction and Dynamic Parameters
- Excitation, Identifiability, and Parameter Correlation
- Independent Validation and Calibration Drift Detection
26World Models and Perception Interfaces10 topics
- Representing Objects, Surfaces, and Free Space
- Geometric and Semantic World Information
- Object Identity, Pose, Shape, and Uncertainty
- Consuming Detections and Pose Estimates from Perception Systems
- Converting Sensor Observations into Robot Frames
- Maintaining Object State Across Observations
- Occlusion, Ambiguity, and Unknown Space
- Observation Freshness and World-Model Consistency
- Task-Relevant Affordances and Interaction Properties
- Requesting Additional Observations Before Acting
27Robot Descriptions and Software Structure11 topics
- Robot Description Files and Kinematic Model Data
- Joint Types, Limits, and Transmission Metadata
- Visual, Collision, and Inertial Representations
- Robot State Publishers and Frame Transform Services
- Driver, Model, Planning, and Task Software Boundaries
- Typed Interfaces for Robot Commands and Observations
- Configuration, Parameters, and Model Versioning
- Component Lifecycle and Dependency Management
- Simulation and Hardware Interface Compatibility
- Namespaces and Multiple Robot Instances
- Automated Consistency Checks for Robot Descriptions
28Communication, Timing, and Data Flow10 topics
- Publish-Subscribe, Request-Response, and Action Interfaces
- Streaming Measurements and Long-Running Robot Commands
- Message Delivery, Ordering, and Queue Behavior
- Sampling Rates and Processing Rates
- Clock Sources and Clock Synchronization
- Timestamp Alignment and Motion Compensation
- Latency, Jitter, and Deadline Budgets
- Buffering, Backpressure, and Stale Data
- Command Timeouts and Communication Loss
- Recording and Replaying Time-Aligned Robot Data
29Robot Simulation and Model Fidelity11 topics
- Kinematic Simulation and Dynamic Simulation
- Building a Robot and Environment Simulation
- Physics Time Steps and Numerical Solver Settings
- Rigid Contact, Compliant Contact, and Friction Models
- Joint Limits, Actuation Limits, and Transmission Models
- Simulating Sensor Noise, Delay, and Dropout
- Initialization and Physically Consistent Robot States
- Deterministic Replay and Sources of Nondeterminism
- Choosing Model Fidelity for a Specific Question
- Comparing Simulation Results with Physical Measurements
- Identifying and Reducing the Simulation-to-Reality Gap
Stage 5
Planning & Manipulation
Getting there, then picking it up
13 modules · 142 topics
30Robot Geometry and Collision Checking11 topics
- Geometric Primitives, Meshes, and Convex Approximations
- Choosing Collision Geometry Independently of Visual Detail
- Broad-Phase and Narrow-Phase Collision Detection
- Self-Collision and Environment Collision
- Distance Queries and Closest-Point Information
- Signed Distance Representations
- Robot Padding and Clearance Margins
- Discrete and Continuous Collision Checking
- Attached Objects and Changing Robot Geometry
- Allowed Contacts and Contact-State-Dependent Collision Rules
- Checking Swept Motion Between Sampled Configurations
31Motion Planning and Graph Search11 topics
- Defining Start States, Goal Sets, and Feasibility Constraints
- Paths, Trajectories, and Executable Motions
- Configuration-Space Obstacles
- Free-Space Connectivity and Narrow Passages
- Configuration-Space Metrics and Interpolation
- Grid and Lattice Representations
- Dijkstra Search and A* Search for Robot Paths
- Heuristics, Search Resolution, and Computational Cost
- Path Length, Clearance, and Task-Specific Objectives
- Completeness, Optimality, and Practical Planning Limits
- Validating a Planned Path Before Execution
32Sampling-Based Motion Planning11 topics
- Configuration Sampling and Feasibility Tests
- Nearest-Neighbor Search in Robot Configuration Spaces
- Local Connections and Steering Functions
- Probabilistic Roadmaps for Repeated Queries
- Rapidly Exploring Random Trees for Single Queries
- Bidirectional Tree Search and Connection Strategies
- Optimal Sampling-Based Planning Variants
- Goal Biasing and Informed Sampling
- Sampling Under Task and Kinematic Constraints
- Narrow-Passage Strategies and Planner Failure Analysis
- Path Simplification, Shortcutting, and Revalidation
33Optimization for Constrained Robot Motion12 topics
- Motion Planning as a Constrained Optimization Problem
- Waypoint, Spline, and Direct-Trajectory Parameterizations
- Smoothness, Effort, Clearance, and Duration Objectives
- Joint, Pose, and Workspace Constraints
- Collision-Distance Constraints and Their Approximation
- Gradients and Automatic Differentiation in Robot Models
- Initialization from Geometric or Sampling-Based Paths
- Local Minima and Infeasible Initial Guesses
- Sequential Convex Approximation of Motion Problems
- Including Dynamic Feasibility in Trajectory Optimization
- Scaling Variables and Checking Solver Residuals
- Independently Validating Optimized Motions
34Trajectory Generation and Time Parameterization12 topics
- Path Geometry and Time Laws
- Point-to-Point Joint Trajectories
- Cubic and Quintic Polynomial Motion Profiles
- Trapezoidal Velocity and Jerk-Limited Profiles
- Cartesian Position and Orientation Trajectories
- Via Points, Splines, and Segment Blending
- Synchronizing Motion Across Multiple Joints
- Velocity, Acceleration, Jerk, and Torque Constraints
- Time Scaling Along a Prescribed Path
- Retiming Paths After Planning or Payload Changes
- Stopping and Resuming a Trajectory Continuously
- Sampling Trajectories for the Robot Command Interface
35Online Replanning and Motion Execution11 topics
- Connecting a Planner to a Motion Executor
- Execution Progress and Tracking Tolerances
- Reconciling Planned State with Measured State
- Moving Obstacles and Time-Dependent Constraints
- Prediction Horizons and Environment Uncertainty
- Replanning Triggers and Update Frequency
- Preserving Continuity When Replacing a Trajectory
- Delayed Plans and Invalidated Planning Assumptions
- Feasible Stopping and Retreat Motions
- Handling Planner Timeouts and Unreachable Goals
- Monitoring Execution Until Task Completion
36Contact Mechanics and Object Interaction10 topics
- Contact Points, Normals, and Tangential Directions
- Unilateral Contact and Nonpenetration
- Static and Kinetic Friction
- Friction Cones and Polyhedral Approximations
- Sticking, Sliding, Rolling, and Separation
- Contact Compliance and Local Deformation
- Multiple Contacts and Contact Mode Combinations
- Quasistatic and Dynamic Interaction Models
- Impact, Impulse, and Changes in Velocity
- Contact Complementarity and Numerical Difficulties
37End-Effectors and Grasp Geometry11 topics
- Choosing an End-Effector from Object and Task Properties
- Parallel-Jaw, Suction, and Multifinger Grippers
- Rigid, Compliant, and Underactuated Gripping Structures
- Jaw Stroke, Finger Geometry, and Object Accessibility
- Contact Surfaces and Material Compatibility
- Grasp Frames, Approach Directions, and Pregrasp Poses
- Geometric Grasp Candidates from Object Models
- Antipodal Grasp Geometry
- Reachability and Collision Checks for Candidate Grasps
- Tool Mounting, Payload, and Utility Interfaces
- Confirming Object Acquisition with Available Measurements
38Grasp Mechanics and Stability10 topics
- Contact Forces and Object Wrench Balance
- Grasp Matrices and Contact Wrench Spaces
- Form Closure and Force Closure
- Internal Grasp Forces and Net Object Motion
- Friction Requirements for Stable Holding
- Gripper Effort Limits and Object Damage Limits
- Gravity and Inertial Loads During Object Transport
- Grasp Quality Metrics and Their Assumptions
- Robustness to Pose, Friction, and Shape Uncertainty
- Slip Detection and Grasp Adjustment
39Manipulation Motion Planning11 topics
- Planning a Complete Acquire-Move-Release Sequence
- Coordinating Grasp Choice with Arm Configuration
- Approach and Retreat Path Constraints
- Transporting Objects with Orientation Restrictions
- Object Placement and Support Stability
- Regrasping and Intermediate Placement Choices
- Manipulation in Clutter and Restricted Spaces
- Using Environmental Supports During Manipulation
- Coordinating Two Arms Around a Shared Object
- Planning Object Handoffs Between Grippers
- Verifying Manipulation Results Before Advancing
40Contact-Rich and Nonprehensile Manipulation11 topics
- Pushing Objects with Controlled Contact Geometry
- Sliding and Pivoting on Supporting Surfaces
- Rolling and Reorienting Objects Through Contact
- Manipulating Hinged and Sliding Objects
- Insertion Tasks and Geometric Alignment
- Jamming, Wedging, and Contact-Induced Failure
- Using Compliance to Accommodate Pose Error
- Contact Search and Incremental Motion Strategies
- Sequencing Contact Modes for a Task
- Monitoring Force and Motion During Interaction
- Recognizing When Rigid-Object Models Are Insufficient
41Task Planning and Motion Planning Integration10 topics
- Task States, Actions, Preconditions, and Effects
- Symbolic Goals and Geometric Requirements
- Decomposing Tasks into Reusable Action Primitives
- Action Dependencies and Ordering Constraints
- Resources, Object Availability, and Tool Requirements
- Connecting Symbolic Actions to Motion Feasibility
- Geometric Failures That Require Task-Level Changes
- Searching Across Grasp, Placement, and Motion Choices
- Planning with Incomplete Task-State Information
- Checking Goal Satisfaction from Physical Evidence
42Behavior Orchestration and Recovery11 topics
- Finite-State Machines for Robot Behavior
- Hierarchical State Machines for Complex Tasks
- Behavior Trees and Reactive Task Execution
- Sequential, Concurrent, and Interruptible Actions
- Action Completion, Failure, and Cancellation Semantics
- Preconditions, Invariants, and Runtime Guards
- Timeouts, Retries, and Bounded Recovery Attempts
- Distinguishing Recoverable and Terminal Failures
- Restoring a Consistent State After Interruption
- Requesting Operator Assistance with Useful Context
- Logging Behavior Transitions for Diagnosis
Stage 6
Mobile Systems & Verification
Wheels, fleets and proof it works
12 modules · 121 topics
43Wheeled Robot Kinematic Foundations10 topics
- Planar Mobile-Robot Pose and Body Velocity
- Wheel Rolling Constraints and Slip Assumptions
- Differential-Drive Forward and Inverse Kinematics
- Unicycle Models and Their Physical Interpretation
- Steering Geometry and Minimum Turning Radius
- Omnidirectional and Mecanum Drive Kinematics
- Holonomic and Nonholonomic Motion Capabilities
- Converting Body-Motion Requests into Wheel Commands
- Wheel-Speed Limits and Feasible Base Motions
- Relating Base Geometry to Maneuverability
44Mobile-Robot Odometry and Navigation Interfaces11 topics
- Integrating Wheel Motion into Pose Estimates
- Odometry Error from Wheel Geometry and Slip
- Combining Wheel and Inertial Measurements
- Local Odometry and Global Reference Frames
- Using External Localization Estimates
- Map Representations Needed by Navigation Modules
- Consuming Maps from Mapping and SLAM Systems
- Robot Footprints, Clearance, and Traversability Inputs
- Sending Pose Goals and Receiving Navigation Status
- Pose Uncertainty, Localization Loss, and Goal Tolerances
- Evaluating Base Navigation as a Robot Subsystem
45Mobile Manipulation10 topics
- Kinematic Models of a Base and Attached Arm
- Frames Across the Base, Arm, Tool, and Environment
- Choosing Base Poses for Manipulation Reachability
- Joint Base-Arm Configuration Planning
- Redundancy Across Base and Arm Motion
- Balancing Arm Dexterity and Base Clearance
- Manipulation with Base-Localization Uncertainty
- Base Stability and Payload-Induced Tipping Constraints
- Coordinating Base Motion with Object Transport
- Repositioning When a Manipulation Task Becomes Infeasible
46Coordinated Multi-Robot Systems10 topics
- Task Decomposition Across Multiple Robots
- Shared and Robot-Specific Coordinate Frames
- Common Object and Task-State Representations
- Allocating Tasks According to Robot Capabilities
- Shared Resources and Mutual Exclusion
- Space-Time Conflicts and Coordinated Motion
- Coupled Motion During Cooperative Object Handling
- Synchronization and Communication Delays
- Deadlock, Stalled Tasks, and Reallocation
- Evaluating Cooperation Over a Single-Robot Baseline
47Data-Driven Robotics and Learned Skills12 topics
- Choosing What to Learn Within a Robot Architecture
- Learning Model Parameters and Residual Errors
- Robot Demonstrations and Action Representations
- Imitation Learning for Bounded Robot Skills
- Reward and Objective Definitions for Skill Learning
- Observation, Action, and Timing Contracts for Policies
- Integrating Learned Skills with Explicit Task Logic
- Task Proposals from General-Purpose Models
- Checking Proposed Actions Against Robot Constraints
- Dataset Coverage and Task-Relevant Variation
- Generalization Across Objects, Poses, and Robot Conditions
- Comparing Learned Skills with Model-Based Baselines
48Computational Performance and Resource Budgets9 topics
- End-to-End Latency Through the Robot Software Stack
- Profiling Kinematics, Collision Checking, and Planning
- Choosing Computation Rates for Different Components
- Caching Reusable Geometry and Model Quantities
- Parallel Computation and Shared-State Consistency
- CPU, GPU, Memory, and Communication Tradeoffs
- Deadline Misses and Graceful Performance Degradation
- Energy and Thermal Budgets for Onboard Computation
- Measuring Performance Under Realistic System Load
49Experimental Design and Robot Performance Evaluation11 topics
- Turning Engineering Questions into Experiments
- Selecting Representative Tasks and Test Conditions
- Position, Orientation, Path, and Timing Metrics
- Task Success, Completion Time, and Intervention Rate
- Repeated Trials and Sources of Variability
- Ground Truth, Reference Instruments, and Measurement Error
- Reporting Distributions and Confidence Intervals
- Sensitivity Studies and Controlled Ablation Experiments
- Separating Component Performance from System Performance
- Benchmark Comparability and Reproducible Test Conditions
- Interpreting Failures Alongside Aggregate Metrics
50Robot Software and Model Verification11 topics
- Testing Transformation and Kinematic Consistency
- Round-Trip Checks for Forward and Inverse Kinematics
- Comparing Analytical and Numerical Derivatives
- Checking Dynamics Through Physical Invariants
- Detecting Invalid Inertial and Geometric Parameters
- Testing Collision Models with Known Geometric Cases
- Verifying Trajectory Bounds and Continuity
- Exercising Behavior Logic with Simulated Events
- Fault Injection for Sensor and Communication Errors
- Software-in-the-Loop and Hardware-in-the-Loop Testing
- Regression Tests Across Robot Model and Software Changes
51System Integration and Prototype Commissioning10 topics
- Integration Plans and Subsystem Entry Criteria
- Checking Mechanical Assembly Against the Robot Model
- Verifying Joint Direction, Scale, and Limits
- Bringing Up Sensors and Checking Frame Alignment
- Establishing Reliable State and Command Communication
- Moving from Individual Joints to Coordinated Motion
- Introducing Tools, Payloads, and Contact Tasks Progressively
- Diagnosing Interface Mismatches Across Subsystems
- Validating Complete Task Sequences on Hardware
- Recording Acceptance Evidence and Open Limitations
52Fault Diagnosis and Robot Health Monitoring10 topics
- Organizing Faults by Observable Symptoms
- Separating Model, Measurement, Planning, and Hardware Faults
- Expected-State Residuals and Diagnostic Signals
- Detecting Friction Changes and Mechanical Wear
- Identifying Encoder, Calibration, and Frame Errors
- Recognizing Timing and Communication Faults
- Monitoring Temperature, Current, and Repeated Saturation
- Detecting Grasp and Tool-Interaction Failures
- Preserving Logs and Reconstructing Failure Sequences
- Maintenance Triggers and Post-Maintenance Validation
53Essential Safe Robot Operation8 topics
- Recognizing Motion, Pinch, Impact, and Stored-Energy Hazards
- Defining Test Boundaries and Permitted Operating Modes
- Understanding Stop Functions and Their Limitations
- Joint, Speed, Effort, and Workspace Limits
- Reduced-Energy Testing and Supervised Initial Motion
- Preventing Unexpected Motion During Setup and Restart
- Handling Tools, Payloads, and Stored Energy During Servicing
- Assigning Stop Authority and Incident Reporting Responsibilities
54Engineering Documentation and Reproducibility9 topics
- Robot Model and Coordinate-Frame Documentation
- Interface Specifications and Command Semantics
- Recording Hardware, Firmware, and Software Configurations
- Calibration Records and Parameter Provenance
- Experiment Manifests and Dataset Organization
- Design Decisions, Assumptions, and Known Limitations
- Reproducible Simulation and Hardware Test Procedures
- Operating, Recovery, and Maintenance Instructions
- Change Review and Revalidation After System Updates
Stage 7
Laboratory & Capstone
Your robot, from model to prototype
3 modules · 31 topics
55Foundation Laboratory Projects10 topics
- Building and Visualizing a Complete Robot Frame Tree
- Modeling a Planar Arm and Mapping Its Workspace
- Implementing Forward Kinematics for a Spatial Manipulator
- Comparing Analytical and Numerical Inverse Kinematics
- Investigating Singularities and Redundant Motion
- Measuring Joint Errors and End-Effector Repeatability
- Identifying a Tool Transform from Measurements
- Predicting Joint Loads for Different Robot Configurations
- Validating a Dynamic Model with Recorded Motion
- Integrating Timestamped Measurements into a Robot State Estimate
56Planning and Manipulation Laboratory Projects10 topics
- Constructing and Testing a Robot Collision Model
- Comparing Graph, Sampling, and Optimization Planners
- Generating Motions Under Joint and Torque Limits
- Replanning After a Simulated Environment Change
- Evaluating Grasp Candidates for a Set of Objects
- Executing an Acquire-Transport-Place Task
- Performing a Constrained Contact-Manipulation Task
- Integrating a Mobile Base with a Manipulator Model
- Building Task Logic with Recovery from Injected Failures
- Comparing Simulated and Physical Task Performance
57Integrated Robotics Engineering Project11 topics
- Defining a Complete Robot Task and Acceptance Criteria
- Selecting an Architecture and Establishing System Interfaces
- Building and Validating the Robot Model
- Establishing Sensing, Frames, and Calibration
- Developing Motion and Manipulation Capabilities
- Implementing Task Execution and Failure Recovery
- Integrating the System in Simulation
- Commissioning a Physical Prototype Within Test Limits
- Evaluating Performance Across Representative Conditions
- Investigating Failures and Revising the Design
- Delivering Reproducible Results and Engineering Documentation
Fifteen minutes.Every day.
- 1
A lesson fits a lunch break
One idea at a time, in short slides. A whole lesson takes about fifteen minutes.
- 2
Practice with instant feedback
Questions sit inside the lesson. Answer one and see right away whether you got it.
- 3
A streak that brings you back
A lesson a day keeps the streak alive. Small, steady sessions carry you through.
- 1
A lesson fits a lunch break
One idea at a time, in short slides. A whole lesson takes about fifteen minutes.
- 2
Practice with instant feedback
Questions sit inside the lesson. Answer one and see right away whether you got it.
- 3
A streak that brings you back
A lesson a day keeps the streak alive. Small, steady sessions carry you through.
Hardware people, software people, both.
Mechanical engineers going robotic
Where you'll grow most
Fuse sensors into a reliable state estimate
Stage 4 · Sensing, Estimation & SoftwareCoders crossing over to hardware
Makers who outgrew the kit
Where you'll grow most
Integrate and commission a working prototype
Stage 6 · Mobile Systems & Verification
Where this course leads.
The job this course is built around, and how people get into it.
Robotics Engineer
Designs robots that sense, decide and move, and makes them reliable outside the lab.
All future careersOn the job
- Integrate sensors, motors and control software
- Tune a controller until the motion is smooth and safe
- Debug a robot that works in simulation but not on the floor
How people get in
Usually a degree in mechanical, electrical or computer engineering.
Be first in line.
Early access for individuals, pilots for teams. Tell us who's learning.
enterprise@astratrainer.com