AI DEVELOPMENT / DEDICATED BUILD
Embodied / Robotic AI
Connect perception, state estimation, planning, and feedback control to physical or simulated action while treating latency, uncertainty, and safety as first-class constraints.
What it is
Connect perception, state estimation, planning, and feedback control to physical or simulated action while treating latency, uncertainty, and safety as first-class constraints.
This page separates the concept, implementation path, interactive experiment, evaluation criteria, failure modes, and sources so the topic can be studied without relying on a summary tile.
Core concepts
- Sensors provide noisy partial observations of the environment.
- State estimation converts observations into a usable belief about position, velocity, objects, or environment state.
- Planning chooses a path or action sequence.
- Controllers turn target states into actuator commands.
- Safety systems bound what actions can occur even when perception or planning is wrong.
Architecture / workflow
- Model the robot, sensors, actuators, limits, and environment.
- Validate perception/state estimation separately from control.
- Test controllers in simulation with noise and latency.
- Add planning and obstacle handling.
- Move to hardware only with explicit speed/force limits, stop mechanisms, logging, and staged validation.
Technical foundations
- Proportional control: u=Kₚ(r−y), often clamped by actuator limits.
- PID control adds integral and derivative terms for accumulated error and damping.
- Kinematics relate joint variables to position/orientation; dynamics add forces and inertia.
- State estimators such as Kalman filters combine a motion model with noisy measurements.
Evaluation checklist
- Tracking error and settling time.
- Collision/constraint violations.
- Robustness to sensor noise, dropped observations, and latency.
- Recovery after blocked paths or actuator saturation.
- Simulation-to-real gap measured on the actual hardware.
Failure modes and limits
- A controller stable in simulation can be unsafe on hardware.
- Perception errors can become motion errors.
- Latency can destabilize feedback loops.
- Mechanical limits, friction, wear, and unmodeled dynamics matter.
Practical build path
- Simulate a one-dimensional controller with noise.
- Add saturation and latency and inspect stability.
- Add a simple planner around obstacles.
- Transfer only after defining hardware limits and emergency-stop behavior.
Primary / authoritative references
AUTHORED STUDY COMPANION / 3.5
Check a reachable target with forward kinematics
Prerequisites. Trigonometry, coordinate frames and workspace constraints.
For two planar unit links, the endpoint is (cos q₁+cos(q₁+q₂), sin q₁+sin(q₁+q₂)). The law of cosines gives cos q₂=(x²+y²−2)/2. A value outside [−1,1] means the requested point is unreachable under this geometry and must be rejected rather than clamped into a fabricated solution.
The companion chooses one elbow branch, solves q₁ and q₂, then independently recomputes the endpoint with forward kinematics. This is position geometry only: it includes no collision map, joint limits, torque, dynamics, feedback control or real robot connection. A reachable point is not automatically a safe motion. Plan a trajectory and validate the omitted constraints before considering physical actuation.
| Element | Model | Interpretation |
|---|---|---|
| Inverse problem | Target → candidate angles | Choose an elbow branch |
| Forward check | Angles → endpoint | Measure residual |
| Missing constraints | Collision, limits, dynamics | No actuation claim |
Predict, run, compare
For target (1,1), one solution is q₁=0 and q₂=π/2. Forward kinematics returns (1,1) with residual near zero; target (3,0) is rejected.
Download executable notebooks and source Inspect source ↗
Open robot.ipynb in the package. Run cells in order, compare with the reference, then change the stated input. Restart the kernel to reset.
Computed reference result — local CPU fixture
{
"joint_radians": [
0.0,
1.5707963267948966
],
"endpoint": [
1.0,
1.0
],
"residual": 0.0,
"scope": "planar position inverse kinematics, one elbow branch; collisions, torque and joint limits omitted"
}This is the recorded result of the included code under the package environment. It is not a live service or device measurement.
Extend the experiment
Compute the second elbow branch. Add joint limits and reject a geometrically reachable point if both solutions violate the limits.
Check your reasoning: A low position residual alone establishes:
- Collision-free motion — No obstacles are modeled.
- Agreement with the stated geometric endpoint — Correct. That is the quantity the residual checks.
- Safe motor torque — No dynamics or actuator limits are modeled.
This is an explained self-check, not a certification of mastery.
Claim-specific sources
Reviewed 2026-10-02: this worked example and its explicit assumptions. Source links and notebook results do not establish production or hardware validation.