Probabilistic Safe Online Learning with Control Barrier Functions

Learning-based control schemes have recently shown great efficacy performing complex tasks. However, in order to deploy them in real systems, it is of vital importance to guarantee that the system will remain safe during online training and execution. We therefore need safe online learning frameworks able to autonomously reason about whether the current information at their disposal is enough to ensure safety or, in contrast, new measurements are required. In this paper, we present a framework consisting of two parts: first, an out-of-distribution detection mechanism actively collecting measurements when needed to guarantee that at least one safety backup direction is always available for use; and second, a Gaussian Process-based probabilistic safety-critical controller that ensures the system stays safe at all times with high probability. Our method exploits model knowledge through the use of Control Barrier Functions, and collects measurements from the stream of online data in an event-triggered fashion to guarantee recursive feasibility of the learned safety-critical controller. This, in turn, allows us to provide formal results of forward invariance of a safe set with high probability, even in a priori unexplored regions. Finally, we validate the proposed framework in numerical simulations of an adaptive cruise control system.

Lyapunov Design for Robust and Efficient Robotic Reinforcement Learning

Recent advances in the reinforcement learning (RL) literature have enabled roboticists to automatically train complex policies in simulated environments. However, due to the poor sample complexity of these methods, solving reinforcement learning problems using real-world data remains a challenging problem. This paper introduces a novel cost-shaping method which aims to reduce the number of samples needed to learn a stabilizing controller. The method adds a term involving a control Lyapunov function (CLF) -- an `energy-like' function from the model-based control literature -- to typical cost formulations. Theoretical results demonstrate the new costs lead to stabilizing controllers when smaller discount factors are used, which is well-known to reduce sample complexity. Moreover, the addition of the CLF term `robustifies' the search for a stabilizing controller by ensuring that even highly sub-optimal polices will stabilize the system. We demonstrate our approach with two hardware examples where we learn stabilizing controllers for a cartpole and an A1 quadruped with only seconds and a few minutes of fine-tuning data, respectively.

Hierarchical Reinforcement Learning for Precise Soccer Shooting Skills using a Quadrupedal Robot

We address the problem of enabling quadrupedal robots to perform precise shooting skills in the real world using reinforcement learning. Developing algorithms to enable a legged robot to shoot a soccer ball to a given target is a challenging problem that combines robot motion control and planning into one task. To solve this problem, we need to consider the dynamics limitation and motion stability during the control of a dynamic legged robot. Moreover, we need to consider motion planning to shoot the hard-to-model deformable ball rolling on the ground with uncertain friction to a desired location. In this paper, we propose a hierarchical framework that leverages deep reinforcement learning to train (a) a robust motion control policy that can track arbitrary motions and (b) a planning policy to decide the desired kicking motion to shoot a soccer ball to a target. We deploy the proposed framework on an A1 quadrupedal robot and enable it to accurately shoot the ball to random targets in the real world.

Collaborative Navigation and Manipulation of a Cable-towed Load by Multiple Quadrupedal Robots

This paper tackles the problem of robots collaboratively towing a load with cables to a specified goal location while avoiding collisions in real time. The introduction of cables (as opposed to rigid links) enables the robotic team to travel through narrow spaces by changing its intrinsic dimensions through slack/taut switches of the cable. However, this is a challenging problem because of the hybrid mode switches and the dynamical coupling among multiple robots and the load. Previous attempts at addressing such a problem were performed offline and do not consider avoiding obstacles online. In this paper, we introduce a cascaded planning scheme with a parallelized centralized trajectory optimization that deals with hybrid mode switches. We additionally develop a set of decentralized planners per robot, which enables our approach to solve the problem of collaborative load manipulation online. We develop and demonstrate one of the first collaborative autonomy framework that is able to move a cable-towed load, which is too heavy to move by a single robot, through narrow spaces with real-time feedback and reactive planning in experiments.

Adapting Rapid Motor Adaptation for Bipedal Robots

Recent advances in legged locomotion have enabled quadrupeds to walk on challenging terrains. However, bipedal robots are inherently more unstable and hence it's harder to design walking controllers for them. In this work, we leverage recent advances in rapid adaptation for locomotion control, and extend them to work on bipedal robots. Similar to existing works, we start with a base policy which produces actions while taking as input an estimated extrinsics vector from an adaptation module. This extrinsics vector contains information about the environment and enables the walking controller to rapidly adapt online. However, the extrinsics estimator could be imperfect, which might lead to poor performance of the base policy which expects a perfect estimator. In this paper, we propose A-RMA (Adapting RMA), which additionally adapts the base policy for the imperfect extrinsics estimator by finetuning it using model-free RL. We demonstrate that A-RMA outperforms a number of RL-based baseline controllers and model-based controllers in simulation, and show zero-shot deployment of a single A-RMA policy to enable a bipedal robot, Cassie, to walk in a variety of different scenarios in the real world beyond what it has seen during training. Videos and results at https://ashish-kmr.github.io/a-rma/

Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models

Bridging model-based safety and model-free reinforcement learning (RL) for dynamic robots is appealing since model-based methods are able to provide formal safety guarantees, while RL-based methods are able to exploit the robot agility by learning from the full-order system dynamics. However, current approaches to tackle this problem are mostly restricted to simple systems. In this paper, we propose a new method to combine model-based safety with model-free reinforcement learning by explicitly finding a low-dimensional model of the system controlled by a RL policy and applying stability and safety guarantees on that simple model. We use a complex bipedal robot Cassie, which is a high dimensional nonlinear system with hybrid dynamics and underactuation, and its RL-based walking controller as an example. We show that a low-dimensional dynamical model is sufficient to capture the dynamics of the closed-loop system. We demonstrate that this model is linear, asymptotically stable, and is decoupled across control input in all dimensions. We further exemplify that such linearity exists even when using different RL control policies. Such results point out an interesting direction to understand the relationship between RL and optimal control: whether RL tends to linearize the nonlinear system during training in some cases. Furthermore, we illustrate that the found linear model is able to provide guarantees by safety-critical optimal control framework, e.g., Model Predictive Control with Control Barrier Functions, on an example of autonomous navigation using Cassie while taking advantage of the agility provided by the RL-based controller.

Perception-aware receding horizon trajectory planning for multicopters with visual-inertial odometry

Visual inertial odometry (VIO) is widely used for the state estimation of multicopters, but it may function poorly in environments with few visual features or in overly aggressive flights. In this work, we propose a perception-aware collision avoidance local planner for multicopters. Our approach is able to fly the vehicle to a goal position at high speed, avoiding obstacles in the environment while achieving good VIO state estimation accuracy. The proposed planner samples a group of minimum jerk trajectories and finds collision-free trajectories among them, which are then evaluated based on their speed to the goal and perception quality. Both the features' motion blur and their locations are considered for the perception quality. The best trajectory from the evaluation is tracked by the vehicle and is updated in a receding horizon manner when new images are received from the camera. All the sampled trajectories have zero speed and acceleration at the end, and the planner assumes no other visual features except those already found by the VIO. As a result, the vehicle will follow the current trajectory to the end and stop safely if no new trajectories are found, avoiding collision or flying into areas without features. The proposed method can run in real time on a small embedded computer on board. We validated the effectiveness of our proposed approach through experiments in indoor and outdoor environments. Compared to a perception-agnostic planner, the proposed planner kept more features in the camera's view and made the flight less aggressive, making the VIO more accurate. It also reduced VIO failures, which occurred for the perception-agnostic planner but not for the proposed planner. The experiment video can be found at https://youtu.be/LjZju4KEH9Q.

Tethered Power Supply for Quadcopters: Architecture, Analysis and Experiments

Tethered quadcopters are used for extended flight operations where the necessary power to the system is provided through the tether from an external power source on the ground. In this work, we study the design factors such as the tether mass, electrical resistance, voltage conversion efficiency, etc. that influence the power requirements. We present analytical formulations to predict the power requirement for a given setup. Additionally, we show the existence of a critical hover height for a single-quadcopter tether system, beyond which it is physically (electrically) impossible for the quadcopter to hover. We then present experimental results for single and two-quadcopter tethered systems. Power supply readings from the experiments in various configurations are consistent with the predictions from the analysis (within 5%), which experimentally validates the presented analysis. A two-quadcopter system powered via a single tether is flown through a corridor to demonstrate one of the applications of having multiple quadcopters on the same tether.

Learning Torque Control for Quadrupedal Locomotion

Reinforcement learning (RL) is a promising tool for developing controllers for quadrupedal locomotion. The design of most learning-based locomotion controllers adopts the joint position-based paradigm, wherein a low-frequency RL policy outputs target joint positions that are then tracked by a high-frequency proportional-derivative (PD) controller that outputs joint torques. However, the low frequency of such a policy hinders the advancement of highly dynamic locomotion behaviors. Moreover, determining the PD gains for optimal tracking performance is laborious and dependent on the task at hand. In this paper, we introduce a learning torque control framework for quadrupedal locomotion, which trains an RL policy that directly predicts joint torques at a high frequency, thus circumventing the use of PD controllers. We validate the proposed framework with extensive experiments where the robot is able to both traverse various terrains and resist external pushes, given user-specified commands. To our knowledge, this is the first attempt of learning torque control for quadrupedal locomotion with an end-to-end single neural network that has led to successful real-world experiments among recent research on learning-based quadrupedal locomotion which is mostly position-based.

Bayesian Optimization Meets Hybrid Zero Dynamics: Safe Parameter Learning for Bipedal Locomotion Control

In this paper, we propose a multi-domain control parameter learning framework that combines Bayesian Optimization (BO) and Hybrid Zero Dynamics (HZD) for locomotion control of bipedal robots. We leverage BO to learn the control parameters used in the HZD-based controller. The learning process is firstly deployed in simulation to optimize different control parameters for a large repertoire of gaits. Next, to tackle the discrepancy between the simulation and the real world, the learning process is applied on the physical robot to learn for corrections to the control parameters learned in simulation while also respecting a safety constraint for gait stability. This method empowers an efficient sim-to-real transition with a small number of samples in the real world, and does not require a valid controller to initialize the training in simulation. Our proposed learning framework is experimentally deployed and validated on a bipedal robot Cassie to perform versatile locomotion skills with improved performance on smoothness of walking gaits and reduction of steady-state tracking errors.