A Response to the Reply Presented in "A Fair Comparison of Sliding-Mode and Immersion-and-Invariance Observers"

Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "A Response to the Reply Presented in "A Fair Comparison of Sliding-Mode and Immersion-and-Invariance Observers"".

Dev: The gist In response to the reply presented in “A Fair Comparison of Sliding-Mode and Immersion-and-Invariance Observers”,

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: We're moving on to what this paper is actually called, which is "A Response to the Reply Presented in 'A Fair Comparison of Sliding-Mode and Immersion-and-Invariance Observers'."

Dev: And the authors are Rosa, Santibáñez, Sandoval, Ortega, and Romero. It’s a team from the Tecnológico Nacional de México / I. T. de La Laguna and other places in Mexico.

Taro: So who are these people? Are they experts in friction modeling or maybe just general control systems?

Rosa: They are field roboticists, so their focus is on testing things outside the lab, figuring out how it works when the world misbehaves, which is right up their alley <ref:2610.20815#pg2>

Dev: And this paper specifically extends some previous research by comparing two observers for a pendular system with nonlinear friction.

Taro: So what does that comparison mean for the broader field of adaptive control? Is it just refining existing methods, or is it pointing toward a new way to approach state estimation?

Rosa: It’s refining the evaluation of position-feedback velocity observers and adaptive tracking controllers in response to earlier work <ref:2610.20815#pg1>

Dev: Essentially, they are taking the ideas from Romero et al. and D´avila et al. and pitting them against each other experimentally on a real physical setup to see which one holds up better under friction conditions <ref:2610.20815#pg2>

Taro: So what are we looking at here? Is this paper just another comparison, or does it suggest a fundamental difference in how you should be estimating the system states?

Rosa: It’s suggesting that for systems with friction, the way you tune your observer gains matters a lot more than just picking a structure <ref:2610.20815#pg3>

Dev: That’s because they showed that one structure, the I andI adaptive observer, gave better results overall and avoided chattering better than the sliding mode ones <ref:2610.20815#pg3>

Taro: So, if you were designing a system today, would you look at this paper to decide between an I andI approach or a sliding mode approach?

Rosa: It tells you that the I andI controller provided the best overall estimation performance and maintained smoothness without visible chatter in their experiments <ref:2610.20815#pg3>

Dev: And they also showed that even when parameter errors are present, you can still get better tracking performance with sophisticated observers like the I andI one compared to simpler methods <ref:2610.20815#pg3>

Taro: So, the implication is that for real-world systems, especially those with nonlinearities like friction, a more robust estimation approach might be necessary than just relying on a single tuning method.

Rosa: It points toward the idea that adaptive observers can be more resilient to changes in operating conditions because they can adjust their internal control parameters based on real-time estimation errors <ref:2610.20815#pg3>

The paper's summary: Dev: Now let’s look at the actual summary of this paper, which boils down to what they did in terms of methodology and what they found about the observers themselves.

Rosa: The core idea is comparing two position-feedback velocity observer structures: the I andI adaptive observer from Romero et al., against the adaptive sliding-mode observer from D´avila et al.

Dev: The I andI observer uses equations three through eight, while the adaptive sliding mode version is given by equations nine through twelve <ref:2610.20815#pg3>

Taro: So what’s the difference in how they are actually structured mathematically? Are we talking about fundamentally different mathematical approaches to state estimation?

Rosa: Yeah, the I andI observer has a set of equations that define how its states and parameters are updated, while the adaptive sliding mode observer is defined by those equations too <ref:2610.20815#pg3>

Dev: The sliding mode observer uses terms like alpha two p x sign in its first equation to update the state estimate, which is a very specific way of handling the switching action <ref:2610.20815#pg3>

Taro: That switching term sounds like it’s trying to force convergence in some specific way, but that brings us back to that issue we talked about earlier regarding the tuning parameters L and alpha one and alpha two <ref:2610.20815#pg1>.

Rosa: Right. The sliding mode observer's tuning procedure involves setting those gains based on a prescription where alpha two = one point five sqrt L and alpha one = 1 point 1L, with L being greater than the supremum of the operation (t) <ref:2610.20815#pg3>

Dev: They emphasize that this reconstruction of should be interpreted as a model-based diagnostic signal, not some kind of an independently established global bound on every perturbation acting on the physical system <ref:2610.20815#pg3>

Taro: So, if you can’t establish that global bound for every possible perturbation, the tuning procedure itself is conditional on something you haven't fully measured yet <ref:2610.20815#pg3>

Rosa: Exactly. And they also found a relationship where dividing alpha two by sqrt alpha one yields a value of one point five sqrt one point one, which only fixes the ratio between observer gains, it doesn't actually eliminate that condition L > t at least zero (t) from the stability analysis <ref:2610.20815#pg3>

Dev: So, they’re saying that the relationship they derived for the gains is just a local fix, not a complete solution to the underlying stability requirement <ref:2610.20815#pg3>

Taro: That means their tuning rules are insufficient on their own to guarantee stability if you don't satisfy that bound condition <ref:2610.20815#pg3>

Rosa: And they also found that the perfect-estimation assumption needed to reduce the closed-loop dynamics to the nominal characteristic equation is not satisfied in their tracking test, which means they can’t just rely on that simple model prediction <ref:2610.20815#pg3>

Dev: So, even with these complex observers, nonzero estimation and parameter-estimation errors mean the system doesn't behave according to its simplest predicted equation <ref:2610.20815#pg3>

Taro: That confirms that for real systems, you have to account for those residual errors when predicting behavior <ref:2610.20815#pg3>

Rosa: So the summary is really about showing that the complexity of friction requires a more nuanced approach than just applying pre-set tuning rules to get a clean result <ref:2610.20815#pg3>

The paper's improvements: Dev: Now let’s talk about the improvements they suggest that stem from this comparison, which are the takeaways for how we can actually use this research to make things better.

Rosa: One improvement is that AI systems could be designed to dynamically adjust their internal control parameters, like observer gains, based on real-time estimation errors instead of relying on a pre-defined, static stability margin <ref:2610.20815#pg3>

Dev: That’s a big shift from having fixed gains when you know that the tuning procedure itself isn't sufficient for guaranteed stability if you don't have that bound condition <ref:2610.20815#pg3>

Taro: So, if AI can adjust those parameters in real time, it means the system doesn’t need to rely on a fixed margin for every possible operating condition <ref:2610.20815#pg3>

Rosa: That means adaptive observers can achieve substantially better tracking performance than what was originally reported in the previous work <ref:2610.20815#pg3>

Dev: And they also maintained smooth and continuous estimate without visible chattering when compared to standard sliding mode observers, which is a key win for robustness <ref:2610.20815#pg3>

Taro: So, the improvement isn't just about better performance; it’s about achieving that smoothness in the estimation process, which makes sense when you are dealing with physical systems <ref:2610.20815#pg3>

Rosa: And another point is that a value of L adjusted from an experimental record might produce satisfactory estimation performance for that specific record, implying the AI system can perform adaptive retuning based on current system excitation <ref:2610.20815#pg3>

Dev: That means the AI isn't stuck with a fixed assumption; it can adapt its own tuning based on how the system is currently being excited <ref:2610.20815#pg3>

Taro: So, that’s where the real resilience comes from, not just in having a static design, but in having a mechanism to adjust parameters as conditions change <ref:2610.20815#pg3>

Rosa: And finally, they show that even when there are nonzero observer and parameter-estimation errors present, the I andI implementation can compensate for those inaccuracies better than simpler methods <ref:2610.20815#pg3>

Dev: So the improvement is showing that sophisticated observers can handle those errors better, rather than just failing when they occur <ref:2610.20815#pg3>

Conclusion: Rosa: So to wrap up, the overall conclusion of this paper is that chattering remains present even when following the tuning rules proposed in

Mu˜noz-V´azquez and S´anchez-Torres(two thousand twenty-six): <ref:2610.20815#pg1,in Mu˜noz-V´azquez and S´anchez-Torres(2026>.

Dev: And they state clearly that satisfying those proposed tuning relationships is not sufficient to guarantee a chattering-free experimental implementation <ref:2610.20815#pg3>

Taro: So the practical takeaway is that you can’t just follow the rules blindly and expect a smooth system response when you’re dealing with friction <ref:2610.20815#pg3>

Rosa: And they say that determining the adequacy of the initially selected value of L can only be done after conducting the experiment and reconstructing <ref:2610.20815#pg3>

Dev: They also state that increasing L produces a larger empirical margin between their reconstructed perturbation and its selected bound, but it doesn't establish a uniform bound for different references or operating conditions <ref:2610.20815#pg3>

Taro: It sounds like the uncertainty about those bounds is something you have to measure out empirically before you can really know if your observer is good enough <ref:2610.20815#pg3>

Rosa: And the overall comparison favored the I andI controller because it showed better results in their tests <ref:2610.20815#pg3>

Dev: The final point is that the nominal characteristic equation alone is not enough to predict actual closed-loop behavior when nonzero observer and parameter-estimation errors are present <ref:2610.20815#pg3>

Taro: So, for our work with multi-robot systems, that means we need strategies that can handle those residual estimation errors in the control loop <ref:2610.20815#pg3>

Rosa: That’s the point of this paper—showing how complex it is when you try to get a clean result from a physical system with nonlinear friction <ref:2610.20815#pg3>

Dev: And that the future direction is moving toward AI-driven control that can adapt its own tuning based on real-time error, not just following static rules <ref:2610.20815#pg3>