Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments

arXiv:2403.02486 · cs.RO, cs.SY, eess.SY · Submitted 2024-03-04 · Read on arXiv

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

Rosa: Today's paper: "Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments".

Dev: This work presents an innovative control algorithm designed to significantly enhance the mobility of underactuated bipedal robots, specifically addressing challenges in navigating non-flat,

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

Title and authors: Dev: So, looking at the title of "Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments," it really highlights the core challenge they were addressing: making these robots move when the terrain isn't just flat.

Rosa: Exactly; it points directly to the difficulty of navigating spaces where foot support is limited, which is a major hurdle for underactuated systems like Cassie.

Taro: And I see they are dealing with both non-flat and non-stationary environments, which suggests they aren't just testing on simple inclines but on things that change while the robot is moving along them.

Dev: That complexity is what makes it interesting from a control engineering standpoint; handling those dynamic changes while maintaining stability at high frequency is always a tough balancing act.

Rosa: What I find particularly compelling about the title, though, is the focus on robust walking rather than just achieving perfect motion in an ideal scenario.

Taro: It suggests the goal isn't just following a pre-set path but maintaining stability even when that path is broken or changing unexpectedly.

Dev: And that robustness has to come from a solid control structure, which leads us directly into what they describe as their dual-strategy controller approach in the abstract.

Rosa: Right, so we’re talking about a method that combines two different ways of controlling the robot's motion to handle these tricky situations.

Taro: I wonder how well that dual approach actually handles scenarios where the expected dynamics break down because of an unforeseen change in environment geometry.

The paper's summary: Rosa: The summary explains that they’ve created a new algorithm by merging ankle torque regulation with a refined angular momentum-based Linear Inverted Pendulum model, which lets them control the center of mass height more flexibly.

Dev: So, essentially, they’re using this ALIP model to manage how high or low the robot's center of mass is allowed to be while still walking stably on these varied surfaces.

Taro: That seems like a sophisticated way to handle the underactuation; instead of trying to perfectly control everything at once, they are using momentum dynamics as a key leverage point.

Rosa: And they employ a dual-strategy controller that mixes virtual constraints for precise motion regulation across certain degrees of freedom with an ALIP-centric Model Predictive Control framework for gait stability.

Dev: The MPC part is where the heavy lifting seems to be, focusing on enforcing those critical gait stability conditions using the ALIP model as its core reference.

Taro: That MPC-centric approach sounds promising for real-time adaptation because it's trying to predict the future state based on momentum, which should help when things change quickly.

Rosa: The paper demonstrates this effectiveness on the Cassie bipedal robot hardware, showing they can achieve speeds up to two point two meters per second on a flat treadmill and maintain speed on inclined surfaces like four degrees and eight degrees.

Dev: Those speed results are impressive, but I want to hear more about how the system handles those transitions between different terrain types mentioned in the summary.

Taro: The summary implies it doesn't require perfect trajectories for every situation, which is something I find very important for real-world autonomy where perfection isn't always possible.

The paper's improvements: Rosa: One of the key improvements they detail is the development of tailored nominal trajectories using the Fast Robot Optimization and Simulation Toolkit, or FROST, which they then approximate using Bézier curves to get those desired paths.

Dev: Utilizing FROST to generate these nominal trajectories across different inclinations, like four degrees up to twenty degrees, shows a systematic way of preparing the system for varied terrains before it even starts moving.

Taro: And what I found interesting is how they used Bézier curves of order five with six control points to define those trajectories; that gives them a lot of fine-grained control over how the robot moves along that path.

Rosa: They also made significant technical improvements to the MPC efficiency, including linearizing impacts around the nominal trajectories and strategically offloading computations to a secondary computer using UDP communication.

Dev: Offloading the computation is smart for meeting those demanding update rates; reducing that calculation time to under five hundred microseconds seems like a necessary step for real-time operation on hardware like Cassie.

Taro: That focus on computational efficiency really helps with the real-time demands, but I wonder if that offloading introduces any new types of latency or communication failures we should be worried about.

Rosa: They also developed an improved impact map based on the linearization of the full-order impact map to reduce those sudden spikes in control output that sometimes happen during hardware experiments.

Dev: Reducing those unexpected spikes is crucial for stability; if you get a huge, sudden torque command because of an unmodeled physical interaction, the whole system can crash or lose balance instantly.

Conclusion: Rosa: So, to wrap up on this paper, it seems they’ve successfully combined these techniques—the ALIP model with the dual-strategy MPC and those optimized trajectory generation methods—to tackle mobility in non-flat, non-stationary environments.

Dev: The main implication for me is that they have proven a feasible path to implementing complex stability control on underactuated hardware that meets stringent real-time frequency requirements.

Taro: From an autonomy standpoint, the implication is that we can move away from relying solely on perfect pre-planning and toward a system that can dynamically adapt its momentum management when the world throws curveballs.

Rosa: I agree; this work shows we don't need every single trajectory perfectly mapped out to achieve stability in complex situations like uneven terrain.

Dev: The paper also points out a limitation, which is that they still rely on those tailored nominal trajectories generated offline; if the actual environment deviates too far from those pre-computed paths, the performance might degrade significantly.

Taro: That reliance on offline planning is a fair caveat; it means we need to think about how quickly the system can generate new plans when it encounters something totally novel.

Rosa: Exactly; this work on demonstrating robust walking in "Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments" gives us a solid foundation for building more resilient locomotion systems.

Oluwami Dosunmu-Ogunbi, Aayushi Shrivastava, Jessy W Grizzle

cs.RO, cs.SY, eess.SY

Submitted: 2024-03-04

Updated: 2024-09-05

DOI: 10.1109/IROS58592.2024.10802406

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 79/100

The gist: This work presents an innovative control algorithm designed to significantly enhance the mobility of underactuated bipedal robots, specifically addressing challenges in navigating non-flat,

Key concepts

Underactuated Bipedal Robots: These are robots with more degrees of freedom (DoF) than they have actuators (motors). They rely on complex dynamics and passive control to achieve stable walking, making them challenging to control in unpredictable environments.
Angular Momentum Linear Inverted Pendulum (ALIP) Model: This is a dynamic model used to predict the robot's motion based on its angular momentum. The authors enhanced this model to better account for changes in the robot's center of mass height, which is crucial when walking on inclines or uneven terrain.
Model Predictive Control (MPC): MPC is a control framework that uses a model to predict future system behavior and calculates the best sequence of actions to follow. In this paper, it was used to enforce gait stability by managing the stance toe actuator and ensuring precise motion regulation.
Dual-Strategy Controller: This controller uses two methods simultaneously: one strategy uses virtual constraints for precise motion regulation, while the second strategy relies on an ALIP-centric MPC framework to maintain overall gait stability during movement.

Terminology

Adaptability — 8× in this paper · explained in 1 episode
Center of Mass — 8× in this paper
Degrees of Freedom — 6× in this paper
Robustness — 6× in this paper · explained in 5 episodes
ALIP-centric Model Predictive Control — 3× in this paper
Angular Momentum Linear Inverted Pendulum — 3× in this paper
Fast Robot Optimization and Simulation Toolkit — 3× in this paper
International Conference on Robotics and Automation — 3× in this paper
Model Predictive Control (MPC) — 3× in this paper · explained in 5 episodes
Sim-to-Real Gap — 3× in this paper · explained in 6 episodes
Center of Mass (CoM) — 2× in this paper · explained in 2 episodes
Core — 2× in this paper · explained in 2 episodes
Passivity-Based Control — 2× in this paper
Quadratic Program — 2× in this paper
Reinforcement Learning — 2× in this paper · explained in 4 episodes
Adaptation — 1× in this paper · explained in 1 episode
Admittance Control — 1× in this paper · explained in 1 episode
Alignment — 1× in this paper · explained in 1 episode
Angular Momentum Linear Inverted Pendulum (ALIP) Model — 1× in this paper · explained in 1 episode
Closed-Loop Control — 1× in this paper · explained in 2 episodes
Hybrid System — 1× in this paper · explained in 2 episodes
Momentum transfer — 1× in this paper · explained in 2 episodes
Ordinary Differential Equation — 1× in this paper
Structural Integrity — 1× in this paper · explained in 3 episodes

Summary

This work presents an innovative control algorithm designed to significantly enhance the mobility of underactuated bipedal robots, specifically addressing challenges in navigating non-flat, non-stationary environments where foot support opportunities are constrained. By combining ankle torque regulation with a refined angular momentum-based Linear Inverted Pendulum model (ALIP), the method allows for variability in the robot’s center of mass height. The approach employs a dual-strategy controller that merges virtual constraints for precise motion regulation with an ALIP-centric Model Predictive Control (MPC) framework to enforce gait stability, successfully demonstrating this capability on the Cassie bipedal robot hardware.

Control Philosophy and System Modeling

The control philosophy is built upon regulating the 20 Degrees of Freedom (DoF) of the Cassie biped, which is inherently underactuated. The system utilizes Passivity-Based Control (PBC) to regulate nine DoF by utilizing nine of Cassie’s actuators to track nominal trajectories generated offline. The tenth actuator is dedicated to regulating one DoF, specifically the stance toe actuator, through an MPC framework. The final DoF is managed via a lateral foot placement approach. To model the dynamics, the paper builds on the Angular Momentum Linear Inverted Pendulum (ALIP) model from [2], [3], enhancing it to better accommodate changes in center of mass (CoM) height as detailed in [1].

Nominal Trajectory Generation

The nominal trajectories are generated using the Fast Robot Optimization and Simulation Toolkit (FROST) [20]. FROST is employed to generate multiple nominal trajectories for Cassie, including those for marching in place, walking forward, and transitioning from flat ground to various inclines (4 degrees, 8 degrees, 15 degrees, and 20 degrees). These trajectories are approximated using Bèzier curves [21], which allows for the finely manipulate these trajectories through adjustments to their control points. A key constraint imposed during generation was one that aimed to minimize torque on the stance ankle motor, a hypothesis which was validated as translating to minimal ankle torque requirements for the physical robot when walking unperturbed.

Enhanced Model Predictive Control (MPC)

A critical enhancement made for hardware implementation involved improving the efficiency of the MPC algorithm. This optimization included:

Linearizing impacts around nominal trajectories.
Strategically offloading computations to a secondary computer and utilizing UDP communication between the secondary computer and Cassie.
Utilizing CasADi, an open-source tool for nonlinear optimization and algorithmic differentiation [24], [25].

This strategic offloading reduced the MPC computation time to under 500 microseconds, which is compatible with Cassie’s stringent controller update frequency of 2 kHz. Furthermore, an improved impact map based on the linearization of the full-order impact map about the nominal trajectories was developed to reduce unexpected spikes in control output during hardware experiments.

Lateral Stabilization Strategy

The lateral motion of the robot is stabilized by using an angular momentum-based foot placement strategy derived from [3], adapted for the new ALIP model. Since the new ALIP model lacks a closed-form solution, a numerical approach was implemented to ensure real-time feasibility on hardware. The strategy involves:

Using Euler method for numerical integration to estimate angular momentum at the end of the next step before impact, yielding values L1 and L2.
Defining a desired angular momentum (Ldes) approximately along the line between Point 1 (y1st→sw, L1) and Point 2 (y2st→sw, L2).
Using 2D or 3D linear interpolation to find ydes, the lateral foot placement position corresponding to Ldes.

This numerical approach was designed so that the execution time for the lateral foot placement controller is less than 5 µs, ensuring adherence to Cassie’s stringent control update frequency. The calculation of the state after impact involves complex equations derived from conservation of angular momentum and CoM velocity, resulting in a defined state vector (Equation 8).

Hardware Validation and Performance

The paper validates the full controller on the physical 20 DoF Cassie bipedal robot hardware across several challenging scenarios:

Maximum Walking Speed: The robot achieved speeds of up to 2.2 m/s on a flat treadmill and maintained speeds of 2 m/s on a treadmill inclined at 4 degrees [27] and 8 degrees [28], reaching up to 1.5 m/s [29], [30] on a 15- and 20-degree slope.
Continuous Walking: The controller demonstrated robustness during continuous walking on a dynamically changing incline, showing that perfect trajectories for all situations are not a prerequisite for stability.
Transitions: The robot successfully navigated transitions from stationary flat ground to an inclined moving treadmill, even accommodating increased treadmill speeds up to 1.

Improvements for AI systems

Here are the specific improvements that can be made to AI systems based on this research, along with what those improved systems could achieve:

The development of a hybrid control architecture combining a high-frequency Passivity-Based Control (PBC) for core dynamics with an optimized, computationally offloaded Model Predictive Control (MPC) framework.
Implementation of a novel angular momentum-based foot placement strategy utilizing real-time numerical integration (Euler method) and pre-computed impact maps to determine lateral stability in underactuated systems.
Integration of trajectory generation techniques leveraging Fast Robot Optimization and Simulation Toolkit (FROST) coupled with Bézier curve manipulation for generating robust nominal trajectories across non-flat, non-stationary terrains.
Creation of a mechanism to dynamically adjust nominal control parameters (e.g., via Bézier control points) in real-time during execution, allowing the system to proactively manage constraints like obstacle avoidance or varying terrain slopes without requiring full offline re-optimization.
Development of a robust Sim-to-Real gap mitigation strategy involving linearization of full-order impact maps around nominal trajectories to prevent unexpected torque spikes during hardware deployment, ensuring stability under real motor friction and sensor inaccuracies.

These improved AI systems can achieve the following:

The system can perform high-speed, stable locomotion on highly complex and dynamic environments (e.g., stairs, uneven terrain) that previously required perfect pre-planning, by adapting its gait in real-time based on momentum dynamics.
It can maintain continuous walking stability while traversing surfaces with rapidly changing inclines or speeds (e.g., moving walkways), effectively handling disturbances and transitions between different operational states without losing balance or exceeding torque limits.
The system will possess enhanced adaptability, allowing it to navigate scenarios where the exact environment geometry is unknown or non-stationary, by using learned nominal trajectories as a flexible baseline rather than rigid paths.
It can operate reliably on physical hardware with stringent real-time constraints (e.g., 2 kHz update frequency) by strategically partitioning computational loads between fast, local controllers and slower, optimized secondary processors for complex planning tasks (MPC).
The resulting AI locomotion system will exhibit superior robustness in unpredictable real-world conditions compared to purely reinforcement learning or open-loop systems, making it suitable for practical applications in disaster management or dynamic human-centric spaces.