Adaptive-MHE : A Sampling-Based Adaptive MPC for Legged Loco-Manipulation via Moving Horizon Estimation

Robots that walk on four legs have become remarkably adept at navigating the messy, uneven world we live in. They can climb over rocks, stride through mud, and recover from slips with a grace that once seemed impossible for machines. However, a significant hurdle remains when these robots are asked to do more than just walk: to push, pull, or carry objects while moving. This dual task, known as loco-manipulation, requires the robot to interact with its environment in complex ways. The difficulty lies in the fact that the physical world is full of unknowns. A robot does not inherently know how heavy a box is, how rough the floor is, or how much friction exists between its feet and the ground. If a robot assumes a box is light when it is actually heavy, or assumes the ground is slippery when it is sticky, its movements will fail. It might slip, drop the object, or become unstable. For a robot to succeed in these uncertain conditions, it cannot rely on a pre-programmed set of rules based on perfect knowledge; it must be able to learn about the physical properties of its surroundings while it is moving.

Researchers have long tried to solve this by teaching robots to guess these properties before they start a task, or by using complex mathematical models that require the robot to calculate the exact physics of every interaction. These traditional methods often struggle because the real world is too chaotic for perfect calculations, especially when a robot's feet are constantly making and breaking contact with the ground. A new approach, developed by a team of engineers, offers a different solution. Instead of trying to calculate the perfect answer from the start, the robot continuously tests many different possibilities in its own mind, compares them to what it is actually feeling, and updates its understanding in real time. This method allows the robot to adapt instantly when the weight of an object changes or when it steps from a smooth floor onto a rough one.

The core of this new system is a framework the researchers call Adaptive-MHE. To understand how it works, imagine a robot pushing a heavy box across a floor. As the robot moves, it records every detail of the interaction: how fast it is moving, how its joints are bending, and how the box responds. The system then runs a rapid, parallel simulation in the background. It generates thousands of different "what if" scenarios. In one scenario, the box might be very light; in another, it might be extremely heavy; in a third, the floor might be covered in ice. The system simulates how the robot would move under each of these different assumptions. It then compares these simulated movements against the actual data the robot is collecting from the real world. The scenario that most closely matches the real-world data is selected as the most likely truth. This process is not a one-time calculation; it happens continuously in a sliding window, constantly refining the robot's estimate of the world as new information arrives.

This estimation process is tightly coupled with the robot's control system. Once the system has a better idea of the box's weight or the floor's friction, it immediately uses that information to adjust the robot's movements. The control system, which decides how the robot's legs should move, uses these updated estimates to plan its next steps. If the robot realizes the box is heavier than it thought, it will automatically apply more force. If it detects the floor is more slippery, it will adjust its stance to maintain balance. The entire loop of sensing, estimating, and acting happens so quickly that the robot appears to react instinctively to changes in its environment. The researchers tested this system on a quadruped robot named the Unitree Go1, which is a commercially available four-legged robot. They placed it in a series of challenging tasks designed to test its ability to handle uncertainty.

In one set of experiments, the robot was tasked with pushing a box toward a specific goal. The researchers introduced sudden changes to the environment to see how the robot would react. In one scenario, the mass of the box was increased by one kilogram while the robot was already pushing it. In another, the robot had to push the box across two different types of flooring: one with a low friction coefficient of 0.4 and another with a high friction coefficient of 0.8. The robot had to detect this change in the floor's texture and adjust its pushing force accordingly without stopping or losing control. The system also tested the robot's ability to push a box using only one leg while keeping the other three legs stationary, a task that requires precise balance and force application.

The results showed that the Adaptive-MHE system significantly outperformed robots that relied on fixed, pre-set assumptions about the environment. When the robot was given a fixed belief about the box's weight or the floor's friction, it failed to complete the task in the majority of trials, often slipping or missing the target. In contrast, the adaptive robot succeeded in nearly 87 percent of the trials, even though it started with no knowledge of the true physical properties. While it did not perform quite as perfectly as a hypothetical robot that knew the exact weight and friction from the very beginning, it came remarkably close. The adaptive robot was able to reduce its error in reaching the goal to a fraction of the distance of the non-adaptive robot. It also completed the tasks faster and with less wasted energy.

The researchers found that the system worked best when it updated its estimates frequently but not so frequently that it became unstable. They tested various settings for how often the robot should re-evaluate the environment and how many different scenarios it should simulate at once. They discovered that a balance was needed: updating the estimates every few seconds allowed the robot to track changes effectively without being overwhelmed by noise in the data. The system was able to identify the mass of the object and the friction of the terrain with high accuracy, even when these properties changed abruptly during the task. This capability suggests that robots can be designed to operate effectively in environments where the physical properties are unknown or constantly shifting, without needing to be retrained for every new situation.

This work represents a significant step forward in making robots more robust and versatile. By combining a method for estimating physical parameters with a controller that can act on those estimates in real time, the researchers have created a system that can handle the unpredictability of the real world. The approach does not require special sensors to measure weight or friction directly; instead, it infers these properties from the robot's own movements and interactions. This makes the technology more practical for deployment in diverse settings, from warehouses to disaster zones, where conditions are rarely known in advance. The success of the Adaptive-MHE framework demonstrates that robots can learn to adapt to their physical surroundings on the fly, bridging the gap between the controlled environment of a simulation and the chaotic reality of the world outside.