On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics

Alessandro De Luca; Claudio Gaz; Giulio Turrisi; Giuseppe Oriolo; Marco Capotondi; Valerio Modugno

REVIEW 3 major objections 4 minor 31 references

On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A two-regressor learning loop lets an underactuated Pendubot swing up in two or three iterations despite 30 percent model errors.

desk verdict A solid, honest extension of the authors' earlier learning-based feedback linearization work to underactuated robots, with real Pendubot experiments; the main gaps are a missing transient guarantee and thin statistics, not a fatal flaw. read the letter →

arxiv 2501.18220 v1 pith:Q6FWCIAJ submitted 2025-01-30 cs.RO

Giulio Turrisi , Marco Capotondi , Claudio Gaz , Valerio Modugno , Giuseppe Oriolo , Alessandro De Luca This is my paper · ORCID

classification cs.RO

keywords underactuatedrobotsmodeluncertaintyGaussianprocessregressionpartialfeedbacklinearizationiterativelearningcontroltrajectoryplanningPendubotswing-up

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes an iterative method that lets an underactuated robot plan and execute a transfer between equilibria when its dynamic model is badly wrong. Each iteration alternates an off-line optimization that plans a trajectory using a learned correction for the passive joints with an on-line controller that tracks that trajectory using a learned correction for the active joints. The claim is that this two-sided learning makes the planned trajectory dynamically feasible and the tracking accurate enough that, after two or three iterations, the Pendubot reaches the basin of attraction of a balancing LQR and completes the swing-up. If true, the approach would remove the usual requirement for an accurate model in underactuated motion planning and control, and would apply to any underactuated robot and any equilibrium-transfer maneuver.

What carries the argument

The load-bearing mechanism is the pair of perturbation equations that result from applying collocated partial feedback linearization to the nominal model. They express the actual accelerations of the active and passive coordinates as the nominal commanded acceleration plus unknown perturbation terms. Each iteration of the algorithm solves an optimal control problem over a prediction model that sets the active perturbation to zero and replaces the passive perturbation with its current estimate, then runs a tracking controller whose commanded active acceleration is the planned feedforward plus PD feedback minus the learned active correction. Gaussian process regressors with squared-exponential kernels are used, one updated in real time for the active term and one updated at the end of each trial for the passive term, the latter reusing all data from previous trials.

What would settle it

Repeat the swing-up simulation with the same 30 percent parameter errors but set the active-side learned correction to zero for the first two iterations while keeping the passive-side learning active; if the maneuver still converges, the active correction is not necessary, and if it fails, the paper's reliance on active perturbation cancellation is confirmed.

Watch

Extended reading notes

Core claim

The central discovery is that model uncertainty in an underactuated robot can be handled by learning two separate perturbation terms rather than by correcting the whole model. After a collocated partial-feedback-linearization control is applied on the nominal model, the perturbed closed-loop dynamics split into an active subsystem, where the uncertainty appears as a term added to the commanded acceleration, and a passive subsystem, where it appears as a term added to the nominal passive acceleration. The paper learns Gaussian-process estimates of these two terms, uses the passive estimate in the planner's prediction model and the active estimate in the tracking controller, and reruns the planning-control loop with warm starts. In simulations with link masses increased by 30 percent and center-of-mass distances reduced by 30 percent, the Pendubot performs a swing-up from the stable down-down equilibrium to the unstable up-up equilibrium after three iterations, and a transfer between two unstable equilibria after two iterations; experiments complete the swing-up in two iterations. The paper states that the same scheme works for a three-link Pendubot with two passive joints and requires no torque measurements.

Load-bearing premise

The planner assumes that the learned active-joint correction will cancel the active perturbation during the control phase, even in the early iterations before the regressor has converged, and the paper provides no formal bound on the error during that transient.

Editorial extensions

If this is right

If the paper is right, a Pendubot can reliably swing up to an inverted equilibrium after two or three learning iterations even when the nominal model overestimates link masses by 30 percent and underestimates center-of-mass distances by 30 percent.
The same two-regressor loop, without modification, handles transfers between unstable equilibria and higher underactuation, such as a 3R Pendubot with two passive joints, suggesting it is not specialized to one maneuver.
Because neither torque measurement nor exact model knowledge is required, the method can be implemented from encoder measurements alone, broadening its applicability to robots without joint torque sensors.
Constraints on states and inputs can be folded into the planning optimization, so the approach can be extended to tasks with obstacles or actuation limits in later iterations.
The paper's comparison indicates that a purely model-based passivity swing-up controller that succeeds with the exact model fails under the same uncertainty, so the learned corrections are what account for the success.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension would be to drive the planner with the full Gaussian-process posterior, using the predictive variance of the passive perturbation in the optimization, which could enforce hard state constraints during the learning transient while still converging in few iterations.
The separation of roles, passive correction in planning and active correction in tracking, suggests a general principle for iterative learning on underactuated systems: plan with the term that shapes the passive dynamics and track with the term that the controller can directly cancel.
If the method generalizes as claimed, similar loops could be applied to other underactuated platforms such as quadrotors or humanoids, where model uncertainty is often significant and planning under dynamic constraints is hard; the authors list these as future targets.
A stress test beyond the paper's 30 percent perturbation, for instance 50 or 60 percent parameter errors, would show whether the iteration count grows gracefully or whether a feasibility barrier appears; the paper does not report such a sweep.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a legitimate and clearly presented extension of the authors' earlier learning-based feedback linearization work to underactuated robots. The split-regressor design—epsilon_p correcting the planner, epsilon_a correcting the controller—is genuinely new relative to their prior fully actuated method and to the closest related work. The empirical claims are supported for the reported runs: the Pendubot reaches the LQR basin after two or three iterations under 30% parameter errors, and the comparisons to the model-based baseline [7] are fair—that method works with the exact model and fails under the same uncertainty. The perturbed dynamics derivation and the data collection formulas are clean, the two experimental scenarios are well chosen, and the simulated 3R case is a useful stress test. Credit where due: the paper does what it claims, honestly, and the writing is refreshingly direct about what was and was not done.

The soft spots are real but not disqualifying. The stress-test note about delta_a = 0 in the planning model (Eq. 7) has genuine teeth. The planner assumes the active perturbation is canceled while learning is still converging, and epsilon_p is trained on data that include the actual acceleration while the planner queries it at u_ref. Early on those arguments can differ by delta_a minus epsilon_a plus PD feedback, so the GP is being queried out of distribution. Table I confirms the transient is non-monotonic: in scenario 1, q2 tracking error goes from 0.191 rad without learning to 0.623 rad at iteration 1 before dropping to 0.038 at iteration 2. The paper provides no bound on that transient, and the authors explicitly list guaranteeing the learning transient as future work. So the concern is not that the paper overclaims—it doesn't—but that the method's convergence behavior is empirically demonstrated rather than formally understood. For a paper advertising 'very few iterations typically,' I would have liked repeated trials and some sensitivity analysis, since swing-up success near a basin boundary can be threshold-sensitive.

The citation pattern is fine; the self-citation to [22] is appropriate because this is a direct extension. No code or data release makes full reproduction harder, but the video and the detailed experimental section help.

This is worth serious refereeing. I would send it out, and I would cite it when discussing learning-based planning and control for underactuated systems. My verdict is conditional rather than unconditional: the authors should address the transient assumption or explicitly scope the claims to the demonstrated runs, and provide at least a small number of repeated trials.

Referee Report

3 major / 4 minor

Summary. The paper proposes an iterative learning framework for planning and control of underactuated robots with uncertain dynamics. Each iteration alternates an off-line optimal control phase, which uses a nominal model corrected by a learned perturbation on the passive subsystem, with an on-line partial-feedback-linearization tracking phase, which uses a learned correction for the active subsystem. The perturbations are estimated from measured trajectories via two Gaussian-process regressors fed by position, velocity, and acceleration data. The method is evaluated on a Pendubot in simulation and on hardware for swing-up maneuvers and transfers between unstable equilibria, under deliberate 30% errors in masses and center-of-mass distances, and it is compared against a passivity-based swing-up controller. The central claim is that after two or three iterations the system enters the LQR basin of attraction and completes the maneuver, and that convergence is achieved in very few iterations despite large model uncertainty.

Significance. If the empirical claims hold, the paper makes a useful contribution: it combines learning with optimization-based planning in a way that does not require torque measurements, is not tailored to a specific underactuated mechanism, and explicitly handles state and input constraints. The derivation of the perturbed active/passive dynamics (Eqs. 5-6) and the data-collection formulas (Eqs. 11-12) are clean and well motivated. The inclusion of both simulations and physical experiments, plus a comparison with a classical model-based method under the same uncertainty, strengthens the demonstration. The main weakness is that the paper's broad convergence claims are supported only by a small number of single-run trials and by an unquantified cancellation assumption in the planner; there is no formal convergence result or statistical repeatability evidence. The method appears promising, but the claim 'convergence is reached ... requiring very few iterations' is stronger than what the presented evidence establishes.

major comments (3)

[§III-A, Eq. (7)] The planning phase sets δ_a = 0 in Eq. (7) and justifies this by the claim that the controller will cancel δ_a via ε_a in Eq. (9). This assumption is load-bearing because the planned trajectory, and hence the feasibility of the transfer and the terminal LQR-basin condition, depends on cancellation being accurate already during the early iterations. The paper provides no bound on ‖δ_a − ε_a‖, no characterization of the transient, and no convergence proof; the Conclusions explicitly defer guarantees on the learning transient to future work. As written, 'convergence is reached' in Section IV-A is an empirical statement about the tested runs, not a property of the algorithm. The authors should either provide a formal or probabilistic guarantee under stated assumptions, or substantially weaken the convergence claims in the abstract and introductory bullets.
[§III-E and §III-A, Eqs. (8) and (12)] There is a training/query distribution mismatch for the passive regressor ε_p. The training data in Eq. (12) use the actual acceleration q̈_a as an input, while the planner in Eq. (8) queries ε_p at q̈_a = u_ref. Before convergence these two arguments differ by δ_a − ε_a plus the PD feedback terms, so the Gaussian process is queried out of distribution during exactly the iterations where the planned trajectory is most likely to be dynamically infeasible. The non-monotonic transient in Table I (scenario 1, q2 RMSE of 0.191 rad without learning, 0.623 rad at iteration 1, then 0.038 rad at iteration 2) indicates that the mismatch can significantly degrade performance before it improves. The paper should either quantify the mismatch and its effect on planning, or present this as a known limitation rather than as a step in a monotone convergence process.
[§IV-B and Table I] The experimental evaluation consists of single runs per scenario and per iteration, with no repeated trials, error bars, or confidence statistics. Given that the active regressor is updated online and that the passive regressor depends on filtered numerical differentiation, run-to-run variability could be substantial. Consequently, the abstract's 'typically' and the bullet 'convergence is reached ... requiring very few iterations' are not supported as statistical statements. The authors should either repeat each experiment several times and report mean/variability, or restrict the claims to 'in the reported trials, convergence was observed after two or three iterations.'

minor comments (4)

[Abstract] There is a typo in the abstract: 'V ery' should be 'Very'.
[§V, Conclusions] The sentence 'Each iteration includes an off-line planning phase and an on-line planning phase' should likely read 'an on-line control phase', consistent with Section III; as written, the sentence describes two planning phases.
[§III-A, second paragraph] The statement that the separate use of one regressor in planning and the other in control 'proves to be computationally more efficient' is not quantified; a brief explanation (e.g., number of optimizer evaluations or real-time constraints) would help the reader assess the claim.
[§IV-A, paragraph after Fig. 7] The 3R Pendubot simulation is only referenced through the accompanying video; providing a quantitative result (e.g., tracking error or number of iterations to convergence) would make the higher-underactuation evidence more verifiable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the learned corrections are empirically identified from measured data, and the success criterion (entering the LQR basin) is independent of the fitted regressors.

full rationale

The paper's derivation chain is not circular. The perturbations δa and δp are defined from the perturbed closed-loop dynamics in Eqs. (5)-(6), and the regressors εa and εp are fitted to measured quantities through Eqs. (11)-(12), namely δa,k = q¨a,k − uk and δp,k = q¨p,k + M̂^{-1}_{pp,k}(n̂p,k + M̂pa,k q¨a,k). These are empirical identifications, not definitions of the target success measure. The planner in Eqs. (7)-(8) uses the learned εp to produce a reference trajectory, while the controller in Eq. (9) uses the learned εa as a corrective feedforward term. The reported success criterion is independent of both regressors: the state must enter the LQR basin |qj,N − qj,g| ≤ 0.2, |q̇j,N| ≤ 0.5, which is neither derived from nor fitted to εa or εp. The main load-bearing assumption is the planner's δa = 0 in Eq. (7), justified by the heuristic that the control term εa in Eq. (9) will cancel δa; this is a transient-correctness gap rather than a circular reduction, and the paper explicitly defers a guarantee to future work ('Future work will consider the problem of guaranteeing hard constraints during the entire learning transient'). The self-citation to [22] is contextual and not load-bearing: the equations, simulations, and experiments in this paper are self-contained, and the method is compared against the independent passivity-based baseline [7]. No claimed prediction reduces to a fitted input by construction, and no load-bearing conclusion is imported solely from the authors' prior work.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central algorithm rests on a handful of engineering choices, GP kernels, cost weights, gains, and terminal tolerances, and on the unproven assumptions that active perturbations can be canceled during planning and that encoder differentiation yields usable perturbation data. No new physical entities are introduced.

free parameters (7)

GP kernel lengthscale l and amplitude a = not reported
Squared exponential kernel hyperparameters, fitted at the end of each iteration; their values and sensitivity are not disclosed.
Cost weights Q, QN, R = not reported
Positive-definite weights in the planning objective, chosen by hand; they shape the planned trajectory and convergence speed.
PD gains KP, KD = KP = 50, KD = 20
Gains in Eq. (9) for active-joint tracking, chosen by the authors and scenario-dependent.
Planning horizon T and sampling time Ts = T = 1.6 s, 0.7 s, 2 s; Ts = 10 ms
Horizon chosen per scenario; affects feasibility and number of iterations.
Terminal constraint tolerances = |qj,N - qj,g| <= 0.2, |dqj,N| <= 0.5 rad/s
Terminal region chosen to match the LQR basin of attraction, 'found to be adequate for all goal states' without analysis.
Velocity bounds = |dq1| <= 8 rad/s, |dq2| <= 15 rad/s
State constraints imposed in the optimization problem.
Reduced set size d for active GP = d = 180
Number of inducing points for real-time active perturbation regression.

assumptions (5)

domain assumption The inertia submatrix M_pp is invertible and the collocated partial feedback linearization (Eq. 4) is well-defined.
Standard for underactuated manipulators with passive joints; invoked in Eq. (4) and throughout.
ad hoc to paper The perturbation functions delta_a and delta_p are smooth functions of their respective inputs and can be represented by a Gaussian process with a squared exponential kernel.
The GP regressors in Sect. III-C assume this structure without structural guarantees; the paper states 'no assumption is made on the structure of the unmodeled dynamics' yet uses a stationary kernel.
ad hoc to paper In planning, setting delta_a = 0 in Eq. (7) is valid because the control loop will cancel delta_a via epsilon_a.
Explicitly stated in Sect. III-A; this transient assumption is load-bearing and unproven.
domain assumption Joint accelerations reconstructed via filtered numerical differentiation of encoder measurements are accurate enough for regression.
Used in Sect. III-D and III-E for data collection; the paper acknowledges filtering but gives no accuracy analysis or error propagation.
domain assumption The nominal model from [31] provides a sufficiently accurate starting point for PFL and planning.
The whole scheme assumes a known nominal model; the paper only tests 30% parameter perturbations, not full model absence.

how reviews work

0 comments

Cite this review

Pith. "Pith review of On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics." pith.science (2026). https://pith.science/paper/Q6FWCIAJ

@misc{pith2026250118220,
  author       = {Pith},
  title        = {Pith review of: On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q6FWCIAJ}},
  note         = {Machine review of arXiv:2501.18220}
}

read the original abstract

We present an iterative approach for planning and controlling motions of underactuated robots with uncertain dynamics. At its core, there is a learning process which estimates the perturbations induced by the model uncertainty on the active and passive degrees of freedom. The generic iteration of the algorithm makes use of the learned data in both the planning phase, which is based on optimization, and the control phase, where partial feedback linearization of the active dofs is performed on the model updated on-line. The performance of the proposed approach is shown by comparative simulations and experiments on a Pendubot executing various types of swing-up maneuvers. Very few iterations are typically needed to generate dynamically feasible trajectories and the tracking control that guarantees their accurate execution, even in the presence of large model uncertainties.

Figures

Figures reproduced from arXiv: 2501.18220 by the authors.

**Figure 2.** Block diagram of the generic iteration of the proposed algorithm. Solid signal lines represent data that are used at each time step, whereas dashed [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The Pendubot and its generalized coordinates. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Simulation scenario 1 (swing-up to q u-u): results without learning. Left: Using the nominal model for planning and the true model for control. Right: Vice versa [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Simulation scenario 1 (swing-up to q u-u): results with the proposed approach. Just before the end of the third iteration, the state has converged to the basin of attraction of the balancing controller, which is then activated (as indicated by the vertical dashed line)…

**Figure 6.** Figure 6: Simulation scenario 1 (swing-up to q u-u): results with the method in [7]. Left: assuming exact model knowledge the state enters the basin of attraction of the LQR controller at t = 1.3 s circa. Right: with the same model uncertainty of [PITH_FULL_IMAGE:figures/full_f…

**Figure 8.** Figure 8: Experimental scenario 1 (swing-up to q u-u): results with the proposed approach. For comparison, the first column shows the results without learning, i.e., when partial feedback linearization and stable tracking for the first joint are computed on the nominal model [P…

**Figure 9.** Figure 9: Experimental scenario 1 (swing-up to q u-u): results with the method in [7]. the obtained reference trajectory and control accuracy (fourth column). Table I offers further insight on the performance in both scenarios. In particular, it shows that the tracking accuracy …

**Figure 10.** Figure 10: Experimental scenario 2 (swing-up to q d-u): results with the proposed approach. Just before the end of the second iteration the state converges to a region where the LQR controller can be successfully activated. The second experiment is again a swing-up scenario, but…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

[7]

Partial stabilization of underactu- ated Euler–Lagrange systems via a class of feedback transformations,

O. Kolesnichenko and A. Shiriaev, “Partial stabilization of underactu- ated Euler–Lagrange systems via a class of feedback transformations,” Systems & Control Lett. , vol. 45, no. 2, pp. 121–132, 2002

work page 2002
[22]

An online learning procedure for feedback linearization control without torque measurements,

M. Capotondi, G. Turrisi, C. Gaz, V . Modugno, G. Oriolo, and A. De Luca, “An online learning procedure for feedback linearization control without torque measurements,” in Proc. Machine Learning Research (3rd Conf. on Robot Learning) , vol. 100, 2020, pp. 1359–1368

work page 2020
[1]

Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators,

G. Oriolo and Y . Nakamura, “Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators,” in Proc. 30th IEEE Conf. on Decision and Control , 1991, pp. 2398– 2403

work page 1991
[2]

Isidori, Nonlinear Control Systems , 3rd ed

A. Isidori, Nonlinear Control Systems , 3rd ed. Springer, 1995

work page 1995
[3]

Underactuated manipulators: Control properties and techniques,

A. De Luca, S. Iannitti, R. Mattone, and G. Oriolo, “Underactuated manipulators: Control properties and techniques,” Machine Intelligence and Robotic Control , vol. 4, no. 3, pp. 113–125, 2002

work page 2002
[4]

Partial feedback linearization of underactuated mechanical systems,

M. Spong, “Partial feedback linearization of underactuated mechanical systems,” in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 1994, pp. 314–321

work page 1994
[5]

Underactuated mechanical systems,

——, “Underactuated mechanical systems,” in Control Problems in Robotics and Automation, B. Siciliano and K. Valavanis, Eds. Springer, 1998, pp. 135–150

work page 1998
[6]

The Pendubot system,

I. Fantoni and R. Lozano, “The Pendubot system,” in Non-linear Control for Underactuated Mechanical Systems . Springer, 2002, pp. 53–72

work page 2002

Show all 31 references

[8]

Swing up and balancing control of Pendubot via model orbit stabilization: Algorithm synthesis and experimental verification,

Y . Orlov, L. T. Aguilar, L. Acho, and A. Ortiz, “Swing up and balancing control of Pendubot via model orbit stabilization: Algorithm synthesis and experimental verification,” in Proc. 45th IEEE Conf. on Decision and Control, 2006, pp. 6138–6143

2006
[9]

Swing-up control of the Pendubot: An impulse–momentum approach,

T. Albahkali, R. Mukherjee, and T. Das, “Swing-up control of the Pendubot: An impulse–momentum approach,” IEEE Trans. on Robotics, vol. 25, no. 4, pp. 975–982, 2009

2009
[10]

Sequential action control: Closed- form optimal control for nonlinear and nonsmooth systems,

A. R. Ansari and T. D. Murphey, “Sequential action control: Closed- form optimal control for nonlinear and nonsmooth systems,”IEEE Trans. on Robotics, vol. 32, no. 5, pp. 1196–1214, 2016

2016
[11]

Hierarchical sliding mode control to swing up a Pendubot,

D. Qian, J. Yi, and D. Zhao, “Hierarchical sliding mode control to swing up a Pendubot,” in Proc. American Control Conf., 2007, pp. 5254–5259

2007
[12]

Fuzzy adap- tive sliding-mode control scheme for uncertain underactuated sys- tems,

S. Moussaoui, A. Boulkroune, and S. Vaidyanathan, “Fuzzy adap- tive sliding-mode control scheme for uncertain underactuated sys- tems,” in Advances and Applications in Nonlinear Control Systems , S. Vaidyanathan and C. V olos, Eds. Springer, 2016, pp. 351–367

2016
[13]

Robot learning,

J. Peters, D. D. Lee, J. Kober, D. Nguyen-Tuong, J. A. Bagnell, and S. Schaal, “Robot learning,” in Springer Handbook of Robotics, 2nd ed., B. Siciliano and O. Khatib, Eds. Springer, 2016, pp. 357–394

2016
[14]

Using model knowledge for learning inverse dynamics,

D. Nguyen-Tuong and J. Peters, “Using model knowledge for learning inverse dynamics,” inProc. IEEE Int. Conf. on Robotics and Automation, 2010, pp. 2677–2682

2010
[15]

Continuous control with deep reinforcement learning,

T. Lillicrap, J. Hunt, A. Pritzel, N. Heess, T. Erez, Y . Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” in Proc. Int. Conf. on Learning Representations , 2016

2016
[16]

PILCO: A model-based and data-efficient approach to policy search,

M. P. Deisenroth and C. E. Rasmussen, “PILCO: A model-based and data-efficient approach to policy search,” in Proc. 28th Int. Conf. on Machine Learning, 2011, pp. 465–472

2011
[17]

Black-box data-efficient policy search for robotics,

K. Chatzilygeroudis, R. Rama, R. Kaushik, D. Goepp, V . Vassiliades, and J.-B. Mouret, “Black-box data-efficient policy search for robotics,” in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems , 2017, pp. 51–58

2017
[18]

Data-efficient control policy search using residual dynamics learning,

M. Saveriano, Y . Yin, P. Falco, and D. Lee, “Data-efficient control policy search using residual dynamics learning,” in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems , 2017, pp. 4709–4715

2017
[19]

Meta learning MPC using finite-dimensional Gaussian process approximations,

E. Arcari, A. Carron, and M. N. Zeilinger, “Meta learning MPC using finite-dimensional Gaussian process approximations,” online https: //arxiv.org/pdf/2008.05984v1.pdf, 2020, published 13 August 2020

2008 arXiv
[20]

Optimization-based iterative learning control for trajectory tracking,

A. Schoellig and R. D’Andrea, “Optimization-based iterative learning control for trajectory tracking,” in Proc. 10th European Control Conf. , 2009, pp. 1505–1510

2009
[21]

Iterative learning of feed- forward corrections for high-performance tracking,

F. L. Mueller, A. Schoellig, and R. D’Andrea, “Iterative learning of feed- forward corrections for high-performance tracking,” in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems , 2012, pp. 3276–3281

2012
[23]

Feedback linearization for uncertain systems via reinforcement learning,

T. Westenbroek, D. Fridovich-Keil, E. Mazumdar, S. Arora, V . Prabhu, S. S. Sastry, and C. J. Tomlin, “Feedback linearization for uncertain systems via reinforcement learning,” in Proc. Int. Conf. on Robotics and Automation, 2020, pp. 1364–1371

2020
[24]

Exploiting differential flatness for robust learning-based tracking control using Gaussian processes,

M. Greeff and A. Schoellig, “Exploiting differential flatness for robust learning-based tracking control using Gaussian processes,” IEEE Control Systems Lett., vol. 5, no. 4, pp. 1121–1126, 2021

2021
[25]

Differential flatness of mechanical control systems: A catalog of prototype systems,

R. M. Murray, M. Rathinam, and W. Sluis, “Differential flatness of mechanical control systems: A catalog of prototype systems,” in Proc. ASME Int. Mechanical Engineering Congr. and Expo , 1995

1995
[26]

Combining deep reinforcement learning and local control for the Acrobot swing-up and balance task,

S. Gillen, M. Molnar, and K. Byl, “Combining deep reinforcement learning and local control for the Acrobot swing-up and balance task,” in Proc. 59th IEEE Conf. on Decision and Control , 2020, pp. 4129–4134

2020
[27]

Motion planning and adaptive neural sliding mode tracking control for positioning of uncertain planar underactuated manipulator,

P. Zhang, X. Lai, Y . Wang, and M. Wu, “Motion planning and adaptive neural sliding mode tracking control for positioning of uncertain planar underactuated manipulator,” Neurocomputing, vol. 334, pp. 197–205, 2019

2019
[28]

Gaussian processes model-based control of underactuated balance robots,

K. Chen, J. Yi, and D. Song, “Gaussian processes model-based control of underactuated balance robots,” in Proc. Int. Conf. on Robotics and Automation, 2019, pp. 4458–4464

2019
[29]

Rasmussen and C

C. Rasmussen and C. Williams, Gaussian Processes for Machine Learn- ing. MIT Press, 2006

2006
[30]

Fast forward selection to speed up sparse Gaussian process regression,

M. Seeger, C. Williams, and N. Lawrence, “Fast forward selection to speed up sparse Gaussian process regression,” in Proc. 9th Int. Work. on Artificial Intelligence and Statistics , 2003

2003
[31]

Enforcing constraints over learned policies via nonlinear MPC: Application to the Pendubot,

G. Turrisi, B. Barros Carlos, M. Cefalo, V . Modugno, L. Lanari, and G. Oriolo, “Enforcing constraints over learned policies via nonlinear MPC: Application to the Pendubot,” IFAC PapersOnLine, vol. 53, no. 2, pp. 9502–9507, 2020

2020

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [7]

Partial stabilization of underactu- ated Euler–Lagrange systems via a class of feedback transformations,

O. Kolesnichenko and A. Shiriaev, “Partial stabilization of underactu- ated Euler–Lagrange systems via a class of feedback transformations,” Systems & Control Lett. , vol. 45, no. 2, pp. 121–132, 2002

work page 2002

[2] [22]

An online learning procedure for feedback linearization control without torque measurements,

M. Capotondi, G. Turrisi, C. Gaz, V . Modugno, G. Oriolo, and A. De Luca, “An online learning procedure for feedback linearization control without torque measurements,” in Proc. Machine Learning Research (3rd Conf. on Robot Learning) , vol. 100, 2020, pp. 1359–1368

work page 2020

[3] [1]

Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators,

G. Oriolo and Y . Nakamura, “Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators,” in Proc. 30th IEEE Conf. on Decision and Control , 1991, pp. 2398– 2403

work page 1991

[4] [2]

Isidori, Nonlinear Control Systems , 3rd ed

A. Isidori, Nonlinear Control Systems , 3rd ed. Springer, 1995

work page 1995

[5] [3]

Underactuated manipulators: Control properties and techniques,

A. De Luca, S. Iannitti, R. Mattone, and G. Oriolo, “Underactuated manipulators: Control properties and techniques,” Machine Intelligence and Robotic Control , vol. 4, no. 3, pp. 113–125, 2002

work page 2002

[6] [4]

Partial feedback linearization of underactuated mechanical systems,

M. Spong, “Partial feedback linearization of underactuated mechanical systems,” in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 1994, pp. 314–321

work page 1994

[7] [5]

Underactuated mechanical systems,

——, “Underactuated mechanical systems,” in Control Problems in Robotics and Automation, B. Siciliano and K. Valavanis, Eds. Springer, 1998, pp. 135–150

work page 1998

[8] [6]

The Pendubot system,

I. Fantoni and R. Lozano, “The Pendubot system,” in Non-linear Control for Underactuated Mechanical Systems . Springer, 2002, pp. 53–72

work page 2002