Combining model-predictive control and predictive reinforcement learning for stable quadrupedal robot locomotion

Stable gait generation is a crucial problem for legged robot locomotion as this impacts other critical performance factors such as, e.g. mobility over an uneven terrain and power consumption. Gait generation stability results from the efficient control of the interaction between the legged robot's body and the environment where it moves. Here, we study how this can be achieved by a combination of model-predictive and predictive reinforcement learning controllers. Model-predictive control (MPC) is a well-established method that does not utilize any online learning (except for some adaptive variations) as it provides a convenient interface for state constraints management. Reinforcement learning (RL), in contrast, relies on adaptation based on pure experience. In its bare-bone variants, RL is not always suitable for robots due to their high complexity and expensive simulation/experimentation. In this work, we combine both control methods to address the quadrupedal robot stable gate generation problem. The hybrid approach that we develop and apply uses a cost roll-out algorithm with a tail cost in the form of a Q-function modeled by a neural network; this allows to alleviate the computational complexity, which grows exponentially with the prediction horizon in a purely MPC approach. We demonstrate that our RL gait controller achieves stable locomotion at short horizons, where a nominal MP controller fails. Further, our controller is capable of live operation, meaning that it does not require previous training. Our results suggest that the hybridization of MPC with RL, as presented here, is beneficial to achieve a good balance between online control capabilities and computational complexity.

Experimental verification of an online traction parameter identification method

Traction parameters, that characterize the ground-wheel contact dynamics, are the central factor in the energy efficiency of vehicles. To optimize fuel consumption, reduce wear of tires, increase productivity etc., knowledge of current traction parameters is unavoidable. Unfortunately, these parameters are difficult to measure and require expensive force and torque sensors. An alternative way is to use system identification to determine them. In this work, we validate such a method in field experiments with a mobile robot. The method is based on an adaptive Kalman filter. We show how it estimates the traction parameters online, during the motion on the field, and compare them to their values determined via a 6-directional force-torque sensor installed for verification. Data of adhesion slip ratio curves is recorded and compared to curves from literature for additional validation of the method. The results can establish a foundation for a number of optimal traction methods.

A stabilizing reinforcement learning approach for sampled systems with partially unknown models

Reinforcement learning is commonly associated with training of reward-maximizing (or cost-minimizing) agents, in other words, controllers. It can be applied in model-free or model-based fashion, using a priori or online collected system data to train involved parametric architectures. In general, online reinforcement learning does not guarantee closed loop stability unless special measures are taken, for instance, through learning constraints or tailored training rules. Particularly promising are hybrids of reinforcement learning with "classical" control approaches. In this work, we suggest a method to guarantee practical stability of the system-controller closed loop in a purely online learning setting, i.e., without offline training. Moreover, we assume only partial knowledge of the system model. To achieve the claimed results, we employ techniques of classical adaptive control. The implementation of the overall control scheme is provided explicitly in a digital, sampled setting. That is, the controller receives the state of the system and computes the control action at discrete, specifically, equidistant moments in time. The method is tested in adaptive traction control and cruise control where it proved to significantly reduce the cost.

On stabilizing reinforcement learning without Lyapunov functions

Reinforcement learning remains one of the major directions of the contemporary development of control engineering and machine learning. Nice intuition, flexible settings, ease of application are among the many perks of this methodology. From the standpoint of machine learning, the main strength of a reinforcement learning agent is its ability to ``capture" (learn) the optimal behavior in the given environment. Typically, the agent is built on neural networks and it is their approximation abilities that give rise to the above belief. From the standpoint of control engineering, however, reinforcement learning has serious deficiencies. The most significant one is the lack of stability guarantee of the agent-environment closed loop. A great deal of research was and is being made towards stabilizing reinforcement learning. Speaking of stability, the celebrated Lyapunov theory is the de facto tool. It is thus no wonder that so many techniques of stabilizing reinforcement learning rely on the Lyapunov theory in one way or another. In control theory, there is an intricate connection between a stabilizing controller and a Lyapunov function. Employing such a pair seems thus quite attractive to design stabilizing reinforcement learning. However, computation of a Lyapunov function is generally a cumbersome process. In this note, we show how to construct a stabilizing reinforcement learning agent that does not employ such a function at all. We only assume that a Lyapunov function exists, which is a natural thing to do if the given system (read: environment) is stabilizable, but we do not need to compute one.

On stochastic stabilization via non-smooth control Lyapunov functions

Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth -- so is the case in non-holonomic systems, like wheeled robots and cars. Frameworks for stabilization using non-smooth control Lyapunov functions exist, like Dini aiming and steepest descent. This work generalizes the related results to the stochastic case. As the groundwork, sampled control scheme is chosen in which control actions are computed at discrete moments in time using discrete measurements of the system state. In such a setup, special attention should be paid to the sample-to-sample behavior of the control Lyapunov function. A particular challenge here is a random noise acting on the system. The central result of this work is a theorem that states, roughly, that if there is a, generally non-smooth, control Lyapunov function, the given stochastic dynamical system can be practically stabilized in the sample-and-hold mode meaning that the control actions are held constant within sampling time steps. A particular control method chosen is based on Moreau-Yosida regularization, in other words, inf-convolution of the control Lyapunov function, but the overall framework is extendable to further control schemes. It is assumed that the system noise be bounded almost surely, although the case of unbounded noise is briefly addressed.

A comment on stabilizing reinforcement learning

This is a short comment on the paper "Asymptotically Stable Adaptive-Optimal Control Algorithm With Saturating Actuators and Relaxed Persistence of Excitation" by Vamvoudakis et al. The question of stability of reinforcement learning (RL) agents remains hard and the said work suggested an on-policy approach with a suitable stability property using a technique from adaptive control - a robustifying term to be added to the action. However, there is an issue with this approach to stabilizing RL, which we will explain in this note. Furthermore, Vamvoudakis et al. seems to have made a fallacious assumption on the Hamiltonian under a generic policy. To provide a positive result, we will not only indicate this mistake, but show critic neural network weight convergence under a stochastic, continuous-time environment, provided certain conditions on the behavior policy hold.

A generalized stacked reinforcement learning method for sampled systems

A common setting of reinforcement learning (RL) is a Markov decision process (MDP) in which the environment is a stochastic discrete-time dynamical system. Whereas MDPs are suitable in such applications as video-games or puzzles, physical systems are time-continuous. Continuous methods of RL are known, but they have their limitations, such as, e.g., collapse of Q-learning. A general variant of RL is of digital format, where updates of the value and policy are performed at discrete moments in time. The agent-environment loop then amounts to a sampled system, whereby sample-and-hold is a specific case. In this paper, we propose and benchmark two RL methods suitable for sampled systems. Specifically, we hybridize model-predictive control (MPC) with critics learning the Q- and value function. Optimality is analyzed and performance comparison is done in an experimental case study with a mobile robot.

An experimental study of two predictive reinforcement learning methods and comparison with model-predictive control

Reinforcement learning (RL) has been successfully used in various simulations and computer games. Industry-related applications, such as autonomous mobile robot motion control, are somewhat challenging for RL up to date though. This paper presents an experimental evaluation of predictive RL controllers for optimal mobile robot motion control. As a baseline for comparison, model-predictive control (MPC) is used. Two RL methods are tested: a roll-out Q-learning, which may be considered as MPC with terminal cost being a Q-function approximation, and a so-called stacked Q-learning, which in turn is like MPC with the running cost substituted for a Q-function approximation. The experimental foundation is a mobile robot with a differential drive (Robotis Turtlebot3). Experimental results showed that both RL methods beat the baseline in terms of the accumulated cost, whereas the stacked variant performed best. Provided the series of previous works on stacked Q-learning, this particular study supports the idea that MPC with a running cost adaptation inspired by Q-learning possesses potential of performance boost while retaining the nice properties of MPC.