TRACE: Learned Proprioceptive Odometry for Legged Robots under Unreliable Contact Conditions

Imagine a robot trying to find its way through a world that doesn't want to be mapped. For decades, scientists have taught robots to navigate using "eyes"—cameras and lasers that scan the scenery for landmarks. But what happens when the lights go out, the fog rolls in, or the robot is walking through a dense forest where the ground is covered in leaves? The "eyes" go blind. This is where the field of proprioceptive odometry comes in. Think of it as the robot's "inner sense," similar to how you can tell if you're walking on a slippery floor or a bumpy path just by feeling the movement in your own muscles and joints, without needing to see your feet. The challenge, however, is that this inner sense is easily tricked. If a robot's foot slips on a wet rock or sinks into soft mud, its internal sensors get confused, and it starts to think it's moving in a straight line when it's actually sliding sideways. Over time, these tiny mistakes pile up, and the robot gets hopelessly lost.

This paper introduces a new solution called TRACE, a smart system designed to help legged robots (like four-legged dogs or humanoids) figure out where they are, even when their feet are slipping, sinking, or rolling on weird terrain. Instead of relying on rigid rules or manual settings to guess if a foot is slipping, TRACE uses a deep learning model that acts like a highly experienced coach. It watches the robot's history of movements and sensor readings, learning to ignore the "noise" of a slipping foot and focus on the "signal" of a solid step. The researchers trained this system in a virtual world full of random chaos—slippery floors, soft mats, and unpredictable bumps—and then tested it on a real robot in the wild. They found that TRACE is significantly better at keeping the robot on track than older methods, reducing the robot's "drift" (the distance it thinks it is from where it actually is) by more than half in some tricky situations.

The Robot's "Inner Ear" Problem

To understand why TRACE is a big deal, we have to look at how robots usually try to count their steps. Imagine you are walking in a dark room with your eyes closed. You try to count your steps to know how far you've gone. If you step on a banana peel and slide, your brain might think you took two steps when you only took one. For a robot, this is a nightmare. If it thinks it moved forward 10 meters but actually only moved 5, it will eventually crash into a wall it thought was far away.

Older methods tried to solve this by using math filters. These filters are like strict teachers who say, "If your foot is on the ground, it must be still." But in the real world, feet aren't always still. They roll, they sink into sand, or they slide on ice. When the "strict teacher" assumes the foot is still but it's actually sliding, the math breaks, and the robot gets lost. Other methods tried to use cameras, but as we mentioned, cameras fail in the dark or in bad weather.

Enter TRACE: The "Smart Coach"

The authors of this paper created TRACE (Tokenized Robust Attention for Contact-Aware Estimation). Instead of a strict teacher, think of TRACE as a smart coach who has watched thousands of hours of robots walking on every kind of surface imaginable.

Here is how it works in simple terms:

1. The Inputs: The robot is constantly sending a stream of data to TRACE: how fast it's spinning (gyroscope), how hard it's accelerating (accelerometer), and the position and speed of every joint in its legs.

2. The "Attention" Trick: This is the magic part. TRACE uses a mechanism called cross-attention. Imagine the robot has four legs, and each leg is shouting its status to the coach.

   • Leg 1 says: "I'm on solid ground! I'm stable!"
   • Leg 2 says: "I'm sliding on ice! I'm useless right now!"
   • Leg 3 says: "I'm sinking into mud!"
   • Leg 4 says: "I'm in the air, swinging!"

   In the past, the robot had to guess which leg to listen to based on a simple rule (like "if the force is low, it's in the air"). TRACE, however, learns to listen. It assigns a "weight" or "attention score" to each leg. If a leg is slipping or sinking, TRACE learns to turn its volume down. If a leg is solid, it turns the volume up. It does this without any human telling it, "Hey, that's a slip!" It just figures out the pattern from the data.

3. The Physics Check: To make sure the robot doesn't just guess wildly, TRACE also has a "physics check." It compares the robot's estimated speed with how far it thinks it moved. If the math doesn't add up (like if the robot says it's moving fast but the legs aren't moving much), the system corrects itself. This is like a runner realizing, "Wait, I'm panting like I'm sprinting, but I haven't moved an inch; I must be running in place."

Training in the Chaos of Simulation

You can't just teach a robot to walk on a single smooth floor and expect it to handle a muddy forest. The researchers trained TRACE in a virtual simulator called RaiSim. But they didn't just make a boring, flat world. They made it chaotic.

• They randomized the terrain: flat ground, stairs, rough rocks, and soft air mattresses.
• They randomized the slip: sometimes the ground was super slippery, sometimes sticky.
• They randomized the robot's movement: they made the robot walk with different styles and speeds.

This is called policy randomization. It's like training a student not just for one specific test, but for every possible variation of the test. By seeing so many different ways the robot could move and slip, TRACE learned to ignore the specific "tricks" of the training and focus on the universal truth of how legs and ground interact.

The Real-World Test

After training in the virtual world, the team took their robot, named Raibo2, out to the real world. They tested it on:

• Flat ground: The easy stuff.
• Rough terrain: Wooden ramps and blocks.
• Slippery surfaces: A board covered in boric acid powder (very slippery!).
• Soft terrain: An air mat that bounces and sinks.
• Outdoor trails: Grass, hard dirt, and stairs.

They compared TRACE against three other methods:

1. IEKF-SR: The old-school "strict teacher" math filter.
2. Legolas: A pure learning-based method that doesn't use physics rules.
3. NMN-IEKF: A hybrid method that tries to mix the two.

The Results: Less Drift, More Confidence

The results were impressive. In the soft terrain experiment (the air mat), where the ground was squishy and unpredictable, TRACE reduced the robot's position error by 53.8% compared to the best previous method. On slippery ground, it reduced the error by 44.1%.

What does this mean? If the other robots thought they were 10 meters away from the start, they might actually be 15 meters away (a huge mistake). TRACE, however, was much closer to the truth. It didn't get confused by the slipping or sinking feet because its "attention" mechanism knew to ignore the unreliable legs.

The researchers also checked if TRACE was actually "paying attention" to the right things. They looked at the data and saw that when a foot was sliding, the system's attention score for that foot dropped to almost zero. When the foot was solid, the score went up. This proved that the robot wasn't just guessing; it was learning to trust the right sensors and ignore the wrong ones.

Why This Matters

The paper concludes that TRACE is a major step forward because it doesn't need a camera to see the world, and it doesn't need a human to program complex rules for every type of slip. It learns to be robust on its own.

However, the authors are careful not to claim this is a "solved" problem. They note that while TRACE is great, it still relies on the quality of the simulation training. They also mention that future work could look at predicting exactly how much a foot is slipping, rather than just ignoring it. But for now, TRACE shows that by teaching robots to "listen" to their bodies with a smart, adaptive ear, we can help them navigate the messy, unpredictable real world without getting lost.

In short, TRACE is like giving a robot a superpower: the ability to know where it is, even when the ground beneath it is lying to it.