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Several studies, for example Rodic and co-workers , have been conducted involving RL as part of the control scheme to control the biped robot. They proposed a novel hybrid control strategy by combining the model-based dynamic controller with RL feedback controller. Guerreo  proposed a supervised RL approach that combined supervised learning (NN) with RL. Experimental results showed that the algorithm was able to be applied on a physical robot to complete the tasks of docking and grasping. However, none of these methods applied RL as the direct joint level controllers, the actions were simply some discrete predefined action samples. The main limitation of their works is that only discrete states and actions were considered, where large errors or oscillations were introduced to the controller. Many recent attempts have been made by Hwang [19,20] with the purpose of applying Q-learning as the joint controller to maintain the balance of the robot of uneven terrains as well as the imitation of human postures. Although continuous actions were generated using Gaussian distribution in their work, the RL structure still relies on a look-up table, meaning that the convergence time would be extremely long. Wu  however, based on Gaussian basis function, employed an abstraction method to reduce the number of state cells needed and applied it on a biped robot to maintain balance on a rotating platform. Simulation results showed that it was able to achieve high precision control with a reduced dimension of state space. One of the major drawbacks to adopting abstraction is that with the generation of the clustering, the actions for each cluster may differ significantly. To achieve better control performance, actions between two nearby clusters (or states) must be transferred smoothly. Seo utilized deep Q-learning (DQN) and the inverted pendulum model (IPM) to control the robot joints to complete the push recovery, where DQN was able to deal with a huge number of states without generating a look-up table or clusters . Shi, in 2020 , employed the deep deterministic policy gradient (DDPG) to improve the precision of attitude tracking control of a biped robot. They proposed an offline pre-training scheme to provide the prior knowledge to the online training in the real physical environment. Garcia, in 2020 , proposed a safe RL algorithm for improving the walking pattern of a NAO robot to allow it to walk faster than the pre-defined configuration. The results showed that their approach was able to increase the learning speed while still reducing the number of falls of the robot during the process of learning. The above methods are all considered as model-free reinforcement learning (MFRL). Although steady state performance can be guaranteed after convergence as no model-induced error is introduced to the system, one major challenge of MFRL is that the convergence time (learning time) is extremely long since no model is used to provide prior knowledge of the system.
As a result, many attempts aiming at combining model-based approaches with model-free learning techniques have been made in recent years. Nagabandi in 2018 proposed a hybrid RL structure that combined NN dynamics models with model predictive control (MPC) to achieve excellent sample complexity in a model-based RL algorithm. Then, they further proposed a NN dynamics model to initialize a model-free learner, where the algorithm guarantees the sample efficiency as well as the control performance . Pong instead combined MFRL with MBRL by introducing the temporal difference models (TDMs) . The proposed RL structure combined the benefits of model-free and model-based RL, where it can be trained with model-free learning and used for model-based control tasks. Feinberg, in 2018, proposed a model-based (MB) value expansion method that incorporated the predictive system dynamics model into model-free (MF) function estimation to reduce sample complexity. According to their algorithm, the predicted dynamics were fitted first, then a trajectory was sampled from the replay buffer to update the actor network, after which an imagined future transition was obtained and was used to update the critic network. Both of the MB and MF parts were used to update the actor and critic network during the learning process . Gu incorporated a particular type of learned model into the proposed Q-learning scheme with normalized advantage functions to improve sample efficiency. They used a mixture of planned iterative LQG and on-policy trajectories, and then generated additional synthetic on-policy rollouts using the learned model from each state visited along the real-world rollouts. At the same time, the model itself was being refit for every n episodes to obtain an effective and data-efficient model learning algorithm . Hafez employed a novel curious meta-controller, where it alternated adaptively between model-based and model-free control. In the end, both the MB planer and MF learner were improved mutually. The method improved the sample efficiency and achieved near-optimal performance . However, these methods were only validated on simple fully-observed models (the walker or the swimmer) under ideal conditions, where no disturbances were added to the environment. They also required a huge amount of computations as both MBRL and MFRL were updated within the iteration during the online learning procedure. In addition, none of the above approaches consider the motor limitations, mechanical constraints, or disturbances. Thus, they are not applicable for physical biped robot joint control tasks to maintain balance as it requires precise joint velocity control at any time step to achieve the minimum steady state error under a dynamic environment.
As a conclusion, first of all, for the model-based RL to achieve a better control performance, the estimated model must be precise enough to contain all information of the system. The problem of it is that it is highly computationally demanding and time consuming to obtain such precise models. Secondly, for the model-free RL, the convergence time is extremely long as there is no prior knowledge of the system for the pure model-free RL. Thirdly, the distribution mismatch problem always exists in other types of HRL frameworks [33,34,35,36]; therefore, to overcome this problem further calculations are required to determine which policy is better, leading to less efficiency of these HRL frameworks. Fourthly, the recent HRL frameworks only validated on simple fully-observed robotic models in ideal environments; thus, they are not suitable for complex biped models such as NAO robots. Thus, a hybrid RL structure has the potential to overcome stability control challenges for biped robots, which has not been fully explored.
To guarantee the fast convergence of MFRL and to achieve the sample efficiency of MBRL, a novel hybrid reinforcement learning framework (HRL) incorporating the inverse kinematics (IK) is introduced in this work, where it successfully establishes a serial connection between MBRL and MFRL. This framework is applied it to a complex biped model (NAO robot) to maintain sagittal and frontal balance on a dynamic platform with disturbances. We combined the hierarchical Gaussian processes (HGP) as the model-based estimator with DQN(λ) as the model-free fine tuning optimizer, where HGP is utilized to predict the dynamics of the system and DQN(λ) is utilized to find the optimal actions. The benefit of using this framework is that the model-based estimator does not need to obtain a very precise dynamic model of the system, which significantly reduces the number of training data as well as the computational load. Secondly, this hybrid structure successfully avoids the distribution mismatch problem (mentioned in ref. [33,34,35,36]) while combining model-based RL with model-free RL. Thirdly, as the estimated model is obtained, and the action space is significantly reduced; therefore, the convergence time of the model-free optimizer is consequently reduced. As a conclusion, the efficiency of the proposed HRL is improved compared with pure model-based RL, pure model-free RL, and other types of HRL approaches. Simulation results show that the proposed algorithm was able to be applied on a NAO robot to maintain balance on a dynamic platform under different oscillations at all times. The adaptability was also guaranteed for the robot on a platform with different rotating frequencies and magnitudes.
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