Grasping, Reachability, and Contact

The camera recognizes a block. The robot reaches it. The fingers close. The block falls. Which part of the reasoning failed?

Recognition, reachability, clearance and holding are different achievements. This lesson asks you to diagnose them separately before calling a grasp successful.

Learning targets

By the end, you can:

1. Distinguish a reachable tip position from a feasible gripper pose and motion.
2. Explain why checking only the endpoint misses collisions.
3. Calculate a symmetric pinch grasp's vertical friction capacity.
4. Reject a mathematically sufficient squeeze when it exceeds a damage or actuator limit.
5. State what the simplified simulation does not prove.

Prerequisites: position and orientation, forward/inverse kinematics, and collision-aware planning. Watch the complete Humanoid Hub tutorial, or use the complete descriptive transcript for an equivalent non-video route.

Learn with the tutorial

Allow about 8 minutes for the 2:30 tutorial, pauses and a short explanation. This is ungraded practice before the lab and quiz. You do not need to finish a calculation during the video's short pause.

Before: make a prediction

At 00:00, a reachable object falls after the fingers close. Write one possible cause and one piece of evidence that would distinguish it from a collision or reachability problem. Keep this first prediction so you can revise it later.

During: follow the mechanism

Times are approximate scene starts in the preserved full tutorial. Watch once for the story; on a second pass, pause at the relevant checkpoint.

Without video: use the same timestamped headings in the descriptive transcript. Read each visual mechanism and spoken explanation, answer the corresponding prompt, then move to the next heading. Stop before “02:09 — Reach. Clear. Hold.” until you have attempted the question. Written, spoken or sketched responses are equally useful; no timed response is required.

After: transfer, then check

For a new simulated object, keep the symmetric static model but use mass 0.6 kg, mu 0.4, and 6 N per pad. Does the vertical load test pass? Show both quantities with units, then state one thing this test cannot establish. Finally, suppose the object's invented limit is 5 N per pad: is the chosen squeeze permitted by that limit?

Self-check after your attempt

Capacity is 2 * 0.4 * 6 = 4.8 N; weight is 0.6 * 9.81 = 5.886 N. Capacity is insufficient in this model. Separately, 6 N per pad exceeds the invented 5 N-per-pad limit. A successful vertical test would still not establish collision clearance, resistance to every torque, or real-hardware safety. If you compared just one pad's capacity with the whole weight, revisit the contact scene; if you changed the weight when changing squeeze, revisit the worked example.

Now revise your opening prediction using evidence, and take that explanation into the Practice lab. Complete the quiz only after the lab; keep the self-check above distinct from the graded quiz answers.

Three checks, not one confidence score

1. Reachability is a geometric question

For our freely rotating planar two-link arm, lengths are 0.6 m and 0.4 m. A tip position at radius 1.06 m is impossible: the links only add up to 1.0 m. A point closer than 0.2 m is also unreachable in this ideal model, because the unequal links cannot fold their lengths away completely.

Thus the position workspace is an annulus, 0.2 <= r <= 1.0 m. This is our original triangle-geometry example, not a robot specification.

Inverse kinematics finds joint angles for a target. Two elbow arrangements can reach many of the same positions. Neither existence nor solver success alone proves that a required wrist orientation or real joint limit is satisfied. MIT's pick-and-place chapter develops the relationship between configuration and gripper pose.

Predict: Does a reachable center point prove a wide gripper can enter a narrow shelf? No: pose, tool geometry and the approach still matter.

2. A clear endpoint can hide a collision

Run the original model. The direct route ends at a reachable position but fails the obstacle test before arriving. Even changing the fingertip route can leave the elbow or forearm in collision.

The supplied detour checks 1,001 poses against a circular obstacle, using two link capsules and a circular gripper envelope. Its smallest sampled clearance is approximately 0.0269 m. That is evidence about this model and sampling—not a continuous collision certificate, a tolerance recommendation, or a complete real-robot plan. The model intentionally omits joint limits, wrist orientation and self-collision.

MoveIt's Planning Scene tutorial distinguishes environment/self-collision checks and kinematic constraints. Our lab is independent original code, not MoveIt.

After grasping, the collision geometry changes: the carried object becomes part of what must clear the surroundings. Check retreat too. The video reminds you of this requirement but does not simulate full carried-object collision geometry.

3. Contact needs a force budget

Imagine a centered 0.5 kg block between two vertical pads. Each pad pushes inward with normal force N. The assumed dry-friction coefficient is mu. Each pad's upward friction capacity is mu * N, so the combined capacity is 2 * mu * N.

For a slow, symmetric vertical lift:

2 * mu * N >= m * g

N means the force from one pad, not the total squeeze from both. With g = 9.81 m/s², weight is 0.5*9.81 = 4.905 N, about 4.9 N.

Friction is not always equal to its maximum. While case B holds the block motionless, total upward friction balances 4.905 N, not 6 N. The remaining capacity is a model margin. See Modern Robotics: Friction for the approximate contact law.

Retrieve: If mass doubles but mu and N stay fixed, which side changes? Weight doubles to 9.81 N; capacity stays 6 N. The previous pass becomes a failure.

4. Passing one inequality is not permission to squeeze harder

Add an invented damage limit of 5 N per pad. Case B requires 6 N per pad, so it must be rejected even though the weight calculation passes. A stronger actuator does not remove the object's limit.

Try changing grasp geometry, using suitable support, reducing the task demand, or stopping for assistance within an approved operating procedure. This simulation does not prescribe hardware force settings.

Real lifting also involves acceleration, torque, contact patches, compliance and uncertain surface conditions. A centered static calculation does not address all of them. MIT's contact treatment separates force and torque balance.

Do not call this a full three-dimensional force-closure test. Two ideal point contacts leave a rotation about their connecting axis unrestrained. Soft contact patches may supply additional moments, but that is a different model. Modern Robotics: Force Closure also explains why a geometric force-closure property does not remove actuator limits.

Your diagnosis

A planner finds joint angles and a collision-free approach. The block slips.

1. Name the missing evidence.
2. Give one measurement or calculation that addresses it.
3. Explain why increasing N is not automatically acceptable.

A strong answer identifies contact forces, compares available friction with load, and checks object/actuator limits. It also states whether torque, motion and uncertainty were considered.

Apply, check, explain

Complete the Practice lab, including the no-code worksheet, then the seven-question quiz. Keep your predictions, measured/calculated evidence and revised explanations.

In one sentence: reach tells you whether a pose is available; clearance tells you whether the motion fits; contact analysis tells you whether the grasp can support the intended load within its limits.