Ayonga Hereid

Yuxiao Chen, Ayonga Hereid, Huei Peng et al.

Correct-by-construction techniques, such as control barrier functions (CBFs), can be used to guarantee closed-loop safety by acting as a supervisor of an existing or legacy controller. However, supervisory-control intervention typically compromises the performance of the closed-loop system. On the other hand, machine learning has been used to synthesize controllers that inherit good properties from a training dataset, though safety is typically not guaranteed due to the difficulty of analyzing the associated neural network. In this paper, supervised learning is combined with CBFs to synthesize controllers that enjoy good performance with provable safety. A training set is generated by trajectory optimization that incorporates the CBF constraint for an interesting range of initial conditions of the truck model. A control policy is obtained via supervised learning that maps a feature representing the initial conditions to a parameterized desired trajectory. The learning-based controller is used as the performance controller and a CBF-based supervisory controller guarantees safety. A case study of lane keeping for articulated trucks shows that the controller trained by supervised learning inherits the good performance of the training set and rarely requires intervention by the CBF supervisor

Yukai Gong, Ross Hartley, Xingye Da et al.

The Cassie bipedal robot designed by Agility Robotics is providing academics a common platform for sharing and comparing algorithms for locomotion, perception, and navigation. This paper focuses on feedback control for standing and walking using the methods of virtual constraints and gait libraries. The designed controller was implemented six weeks after the robot arrived at the University of Michigan and allowed it to stand in place as well as walk over sidewalks, grass, snow, sand, and burning brush. The controller for standing also enables the robot to ride a Segway. A model of the Cassie robot has been placed on GitHub and the controller will also be made open source if the paper is accepted.

Ayonga Hereid, Omar Harib, Ross Hartley et al.

One of the big attractions of low-dimensional models for gait design has been the ability to compute solutions rapidly, whereas one of their drawbacks has been the difficulty in mapping the solutions back to the target robot. This paper presents a set of tools for rapidly determining solutions for ``humanoids'' without removing or lumping degrees of freedom. The main tools are (1) C-FROST, an open-source C++ interface for FROST, a direct collocation optimization tool; and (2) multi-threading. The results will be illustrated on a 20-DoF floating-base model for a Cassie-series bipedal robot through numerical calculations and physical experiments.

Zhaoyang Xiang, Upama Pant, Ayonga Hereid

Many real-world walking scenarios contain obstacles and unsafe ground patches (e.g., slippery or cluttered areas), leaving a disconnected set of admissible footholds that can be modeled as stepping-stone-like regions. We propose an onboard, perceptive mixed-integer model predictive control framework that jointly plans foot placement and step duration using step-to-step Divergent Component of Motion (DCM) dynamics. Ego-centric depth images are fused into a probabilistic local heightmap, from which we extract a union of convex steppable regions. Region membership is enforced with binary variables in a mixed-integer quadratic program (MIQP). To keep the optimization tractable while certifying safety, we embed capturability bounds in the DCM space: a lateral one-step condition (preventing leg crossing) and a sagittal infinite-step bound that limits unstable growth. We further re-plan within the step by back-propagating the measured instantaneous DCM to update the initial DCM, improving robustness to model mismatch and external disturbances. We evaluate the approach in simulation on Digit on randomized stepping-stone fields, including external pushes. The planner generates terrain-aware, dynamically consistent footstep sequences with adaptive timing and millisecond-level solve times.

Lokesh Krishna, Guillermo A. Castillo, Utkarsh A. Mishra et al.

In this work, we demonstrate robust walking in the bipedal robot Digit on uneven terrains by just learning a single linear policy. In particular, we propose a new control pipeline, wherein the high-level trajectory modulator shapes the end-foot ellipsoidal trajectories, and the low-level gait controller regulates the torso and ankle orientation. The foot-trajectory modulator uses a linear policy and the regulator uses a linear PD control law. As opposed to neural network-based policies, the proposed linear policy has only 13 learnable parameters, thereby not only guaranteeing sample efficient learning but also enabling simplicity and interpretability of the policy. This is achieved with no loss of performance on challenging terrains like slopes, stairs and outdoor landscapes. We first demonstrate robust walking in the custom simulation environment, MuJoCo, and then directly transfer to hardware with no modification of the control pipeline. We subject the biped to a series of pushes and terrain height changes, both indoors and outdoors, thereby validating the presented work.

Lokesh Krishna, Utkarsh A. Mishra, Guillermo A. Castillo et al.

In this paper, with a view toward deployment of light-weight control frameworks for bipedal walking robots, we realize end-foot trajectories that are shaped by a single linear feedback policy. We learn this policy via a model-free and a gradient-free learning algorithm, Augmented Random Search (ARS), in the two robot platforms Rabbit and Digit. Our contributions are two-fold: a) By using torso and support plane orientation as inputs, we achieve robust walking on slopes of up to 20 degrees in simulation. b) We demonstrate additional behaviors like walking backwards, stepping-in-place, and recovery from external pushes of up to 120 N. The end result is a robust and a fast feedback control law for bipedal walking on terrains with varying slopes. Towards the end, we also provide preliminary results of hardware transfer to Digit.

Guillermo A. Castillo, Bowen Weng, Wei Zhang et al.

In this paper, a hierarchical and robust framework for learning bipedal locomotion is presented and successfully implemented on the 3D biped robot Digit built by Agility Robotics. We propose a cascade-structure controller that combines the learning process with intuitive feedback regulations. This design allows the framework to realize robust and stable walking with a reduced-dimension state and action spaces of the policy, significantly simplifying the design and reducing the sampling efficiency of the learning method. The inclusion of feedback regulation into the framework improves the robustness of the learned walking gait and ensures the success of the sim-to-real transfer of the proposed controller with minimal tuning. We specifically present a learning pipeline that considers hardware-feasible initial poses of the robot within the learning process to ensure the initial state of the learning is replicated as close as possible to the initial state of the robot in hardware experiments. Finally, we demonstrate the feasibility of our method by successfully transferring the learned policy in simulation to the Digit robot hardware, realizing sustained walking gaits under external force disturbances and challenging terrains not included during the training process. To the best of our knowledge, this is the first time a learning-based policy is transferred successfully to the Digit robot in hardware experiments without using dynamic randomization or curriculum learning.

Guillermo A. Castillo, Bowen Weng, Terrence C. Stewart et al.

This paper presents a neural-network based adaptive feedback control structure to regulate the velocity of 3D bipedal robots under dynamics uncertainties. Existing Hybrid Zero Dynamics (HZD)-based controllers regulate velocity through the implementation of heuristic regulators that do not consider model and environmental uncertainties, which may significantly affect the tracking performance of the controllers. In this paper, we address the uncertainties in the robot dynamics from the perspective of the reduced dimensional representation of virtual constraints and propose the integration of an adaptive neural network-based controller to regulate the robot velocity in the presence of model parameter uncertainties. The proposed approach yields improved tracking performance under dynamics uncertainties. The shallow adaptive neural network used in this paper does not require training a priori and has the potential to be implemented on the real-time robotic controller. A comparative simulation study of a 3D Cassie robot is presented to illustrate the performance of the proposed approach under various scenarios.

Guillermo A. Castillo, Bowen Weng, Wei Zhang et al.

This paper presents a novel model-free reinforcement learning (RL) framework to design feedback control policies for 3D bipedal walking. Existing RL algorithms are often trained in an end-to-end manner or rely on prior knowledge of some reference joint trajectories. Different from these studies, we propose a novel policy structure that appropriately incorporates physical insights gained from the hybrid nature of the walking dynamics and the well-established hybrid zero dynamics approach for 3D bipedal walking. As a result, the overall RL framework has several key advantages, including lightweight network structure, short training time, and less dependence on prior knowledge. We demonstrate the effectiveness of the proposed method on Cassie, a challenging 3D bipedal robot. The proposed solution produces stable limit walking cycles that can track various walking speed in different directions. Surprisingly, without specifically trained with disturbances to achieve robustness, it also performs robustly against various adversarial forces applied to the torso towards both the forward and the backward directions.

Guillermo A. Castillo, Bowen Weng, Ayonga Hereid et al.

The design of feedback controllers for bipedal robots is challenging due to the hybrid nature of its dynamics and the complexity imposed by high-dimensional bipedal models. In this paper, we present a novel approach for the design of feedback controllers using Reinforcement Learning (RL) and Hybrid Zero Dynamics (HZD). Existing RL approaches for bipedal walking are inefficient as they do not consider the underlying physics, often requires substantial training, and the resulting controller may not be applicable to real robots. HZD is a powerful tool for bipedal control with local stability guarantees of the walking limit cycles. In this paper, we propose a non traditional RL structure that embeds the HZD framework into the policy learning. More specifically, we propose to use RL to find a control policy that maps from the robot's reduced order states to a set of parameters that define the desired trajectories for the robot's joints through the virtual constraints. Then, these trajectories are tracked using an adaptive PD controller. The method results in a stable and robust control policy that is able to track variable speed within a continuous interval. Robustness of the policy is evaluated by applying external forces to the torso of the robot. The proposed RL framework is implemented and demonstrated in OpenAI Gym with the MuJoCo physics engine based on the well-known RABBIT robot model.

Omar Harib, Ayonga Hereid, Ayush Agrawal et al.

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.