Cited by 138Robot Manipulation and LearningReinforcement Learning in RoboticsSoft Robotics and Applications

Learning from Demonstrations Through the Use of Non-rigid Registration

Schulman, John, Ho, Jonathan, Lee, Cameron, Abbeel, Pieter·2016·Springer Tracts in Advanced Robotics

AI snapshot

Written from the paper’s full text.

TL;DR

The paper presents trajectory transfer, a method that adapts a demonstrated end-effector trajectory to a new scene by non-rigidly registering the training point cloud to the test point cloud and warping the trajectory accordingly. It validates the approach mainly by enabling a PR2 robot to tie five knot types from demonstrations, and also shows qualitative results on other manipulation tasks.

Key findings

  • With one demonstration per knot, success under random rope perturbations depended on perturbation size: at \(d_{pert}=3\) cm, success was 5/5 for overhand, figure-eight, and square, 3/5 for double-overhand, and 1/5 for clove hitch; at \(d_{pert}=10\) cm, success was 4/5, 1/5, 3/5, 3/5, and 0/5 respectively.
  • The PR2 autonomously tied five knot types: overhand, figure-eight, double-overhand, square knot, and clove hitch around a pole.
  • For the overhand knot, the authors collected 148 trajectory segments, including 36 demonstrations of the standard 3-step sequence and 40 additional segments starting from failure states; the nearest-neighbor policy was qualitatively able to tie knots from a larger set of initial configurations and recover from failure states.
  • The same algorithm and code were applied to folding a T-shirt, picking up a plate with a two-arm motion, and opening a bottle, with qualitative success reported.

Methods

  • Trajectory transfer: register the training scene point cloud to the test scene point cloud using a modified TPS-RPM non-rigid registration algorithm, then apply the resulting transformation \(f\) to demonstrated end-effector positions and use the Jacobian \(Jf(p)\) to transform orientations.
  • Convert the transferred end-effector trajectory into a joint trajectory by solving an optimization problem that trades off smoothness, end-effector pose error, collision avoidance, and joint limits, using the trajectory optimization method from Schulman et al. and initializing from the demonstration.
  • For multi-step tasks, repeatedly choose the nearest demonstration by registration cost, apply trajectory transfer, and execute the resulting trajectory; experiments used a PR2 with kinesthetic teaching and RGBD point clouds, with rope points extracted by color filtering.

Limitations

  • The paper states that the cost-function invariance assumption in Equation (7) is strong and can fail even for rigid transformations, for example when absolute end-effector orientation matters.
  • The paper states that dynamics covariance holds only approximately in knot tying and was checked qualitatively by comparing final rope states at training and test time.
  • The paper reports only qualitative results for the many-demonstration overhand knot policy and for the other manipulation tasks; no quantitative success rates are given for those settings. The single-demonstration results also show low success for clove hitch and for larger perturbations.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/978-3-319-28872-7_20

Cites

34 of 34 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 4 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § Learning from Demonstrations Through the Use of Non-Rigid Registration · p. 1

    A PR2 robot autonomously tied five different types of knots in rope: overhand, figure-eight, double-overhand, square knot, and clove hitch (around a pole).

    “As our main experimental validation, we enable a PR2 robot to autonomously tie five different types of knots in rope.”
    • Also stated in: § 5 Experiments with rope · p. 9 · plain
      “We enabled the PR2 to autonomously tie five different types of knot: overhand, figure-eight, double-overhand, square knot, and clove hitch (around a pole).”
    Quote in the paperSubstantial claim
  • Findingnone given
    § 1 Introduction · p. 2

    The nearest-neighbor policy recovers from failures, provided that the demonstrator has provided examples of the failure states along with the corrective motions that get out of them.

    “This policy recovers from failures, assuming that the demonstrator has provided examples of the failure states along with the corrective motions that get out of them.”
    • Also stated in: § 4 Generalizing from many examples: nearest neighbor method · p. 9 · plain
      “This policy enables the robot to recover from errors, provided that the demonstrator has provided a demonstration starting from the failure state.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The demonstrator has provided examples of the failure states along with the corrective motions that get out of them.
  • Findingown data
    § 5 Experiments with rope · p. 10

    The nearest-neighbor policy is able to choose corrective movements to recover from the failure states.

    “and it is also able to choose corrective movements to recover from the failure states.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 9.1 Thin plate splines · p. 15

    The regularization r(B) was necessary because sometimes the transformation is underdetermined in certain dimensions.

    “We found that the regularization r ( B ) was necessary because sometimes the transformation is underdetermined in certain dimensions.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 7 Conclusion · p. 12

    The method successfully picked up a plate when the training round plate was registered to a rectangular plate at test time.

    “Bottom row, left: demonstration and autonomous execution of plate pickup. Round plate from training was registered to rectangular plate at test time.”
    Quote in the paperSubstantial claim
  • May combine two claims. 5
  • The quote only partly states this claim. 1
  • Classified as probably not a substantial claim. 4
  • May combine two claims.

    Findingown data
    § 5 Experiments with rope · p. 10

    A common failure mode was that the robot would grab the wrong piece of rope, or two pieces instead of one.

    “Two of the common failure modes were (1) the rope would end up in a previously unseen crossing state, often due to a small difference in its position; (2) the robot would grab the wrong piece of rope, or two pieces instead of one.”
    Quote in the paperNot a substantial claim
  • The quote only partly states this claim.

    Findingown data
    § 7 Conclusion · p. 12

    The method successfully opened a bottle whose size and shape differed from the one used for training.

    “Bottom row, right: demonstration and autonomous execution of bottle opening. The bottle used at test time had a different size and shape from the one used for training.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data
    § 3.3.2 Dynamics invariance · p. 8

    Assumption 4, that the dynamics are covariant under f, holds approximately in the knot tying domain; this was checked qualitatively by comparing the final states of the rope at training and test time.

    “Assumption 4 holds approximately in this domain; we have checked this qualitatively by comparing the final states of the rope at training and test time.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data
    § 3.2 Trajectory transfer procedure · p. 6

    Inverse kinematics alone is not sufficient for converting the transferred end-effector trajectory into a joint trajectory because there is often no continuous and collision-free trajectory that achieves the desired end-effector trajectory.

    “We found that this approach was not sufficient because there is often no continuous and collision-free trajectory that achieves the desired end-effector trajectory, so we need to compromise.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § 9.1 Thin plate splines · p. 15

    With the quadratic regularization term r(B)=trace((B-I)^T D (B-I)), the optimization problem still can be solved analytically as a least squares problem.

    “With this quadratic regularization term, the optimization problem still can be solved analytically as a least squares problem.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 3.3.1 Cost function invariance · p. 7

    There exist situations where the cost function invariance assumption (Equation 7) does not hold, even for a rigid transformation f, for example when absolute orientation of the robot's end-effector matters.

    “That said, one can imagine situations where Equation (7) does not hold, even for a rigid transformation f -for example, when absolute orientation of the robot's end-effector matters.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 3.1.1 Registration with known correspondences · p. 4

    Equation (1) can be analytically solved efficiently.

    “As shown in [18], Equation (1) can be analytically solved efficiently; details are provided in Appendix 9.1.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [18] Wahba, G.: Spline models for observational data, Society for Industrial Mathematics, vol. 59 (1990) source
  • May combine two claims.

    Interpretationown data
    § 5 Experiments with rope · p. 10

    When starting from a state that is very close to a demonstration, the success rate is high, at least for the easier knots.

    “The above results suggest that when starting from a state that is very close to a demonstration, the success rate is high, at least for the easier knots.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § 3.3.2 Dynamics invariance · p. 8

    In the knot tying domain, the goal set is defined topologically, and a transformation f will preserve it, provided that it is a homeomorphism.

    “In the knot tying domain, the goal set is defined topologically, and a transformation f will preserve it, provided that it is a homeomorphism (i.e., a continuous function whose inverse is continuous), justifying assumption 3.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationreasoning
    § 2 Related work · p. 3

    Our approach operates directly on point clouds and is suitable for knot tying, and it can be applied to a new task without developing a new vision system.

    “In contrast, our approach operates directly on point clouds-the outputs of our sensor hardware-so it is suitable for this task, and it can be applied to a new task without developing a new vision system.”
    Quote in the paperSubstantial claim
10 of 10
  • The authors state this as an assumption.

    The demonstrator has provided examples of the failure states along with the corrective motions that get out of them.

    “This policy recovers from failures, assuming that the demonstrator has provided examples of the failure states along with the corrective motions that get out of them.”
  • The authors state this as an assumption.

    There exists a class of smooth transformations f such that L(STATE, TRAJ) = L(f(STATE), f(TRAJ)).

    “Our trajectory transfer procedure can be justified by assuming that there is a class of smooth transformations f with the following property:”
  • The authors state this as an assumption.

    The dynamics of the system are covariant under the transformation f (Equation 10 holds).

    “4. Equation (10) holds, i.e., the dynamics are covariant under f .”
  • The authors state this as an assumption.

    The goal set is preserved by f (f(G)=G).

    “3. f ( G ) = G , i.e., the goal set is preserved by f”
  • The authors state this as an assumption.

    f transforms STATE_train into STATE_test (f(STATE_train)=STATE_test).

    “1. f ( STATE t train ) = STATE t test , i.e., f transforms STATE train into STATEtest.”
  • The authors state this as an assumption.

    The demonstration ends up in the goal state (STATE_{t+1}^{train} ∈ G).

    “2. STATE t + 1 train ∈ G , i.e., the demonstration ends up in the goal state.”
  • The paper relies on this without support.

    For each segment, the end-effector trajectory depends on the geometry of the rope in some way that must be inferred by the algorithm.

    “For each of these segments, the end-effector trajectory ought to depend on the geometry of the rope in some way that must be inferred by the algorithm.”
  • The paper relies on this without support.

    The procedure for tying a given type of knot can be broken into several segments based on grab and release events.

    “The procedure for tying a given type of knot can be broken into several segments based on grab and release events.”
8 of 8

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Authors
Schulman, J., Ho, J., Lee, C., & Abbeel, P.
Affiliations
University of California, Berkeley (US)
Corresponding author
Schulman, John
Venue
Springer Tracts in Advanced Robotics
Published
2016
Pages
339-354
ISSN
  • 1610-742X (ISSN-L)
  • 1610-7438
OpenAlex
W2472053385
Cited by
133
References
31
Citations by year
2026: 1 · 2025: 4 · 2024: 4 · 2023: 9 · 2022: 14 · 2021: 15 · 2020: 18 · 2019: 12 · 2018: 18 · 2017: 13 · 2016: 6 · 2015: 13 · 2014: 6
FWCI
38.92
Type
book chapter
Language
en
Open access
closed
Locations
Springer tracts in advanced robotics (publishedVersion)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Robot Manipulation and Learning
  • Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
  • Physical Sciences › Engineering › Biomedical Engineering › Soft Robotics and Applications
Keywords
imitation learning, non-rigid registration, robotic manipulation, multi-step tasks, PR2 robot, knot tying, rope manipulation

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