The gait data used in this study are also normal gait data collected from Ekkachai and Nilkhamhang (2016) for convenience in comparison study of the controller. An active mechanism can generate a net positive force. Syst. The mathematical descriptions of the proposed designed reward functions are expressed in Equations (7)–(11). This problem is also known as the credit assignment problem. In this study, the control policy that we train is valid only for the subject whose data we used. A reward shaping technique based on the Lyapunov stability theory proposed in accelerates the convergence of RL algorithms. Med. Therefore, from the cost-effective and functionality point of view, a semi-active prosthetic knee is still more favorable for the end user compared to the active mechanism. Control Syst. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. Each will be reviewed in depth in the following sections. Based on the data used, the state θK(t) is within the range of 0 and 70° with a predefined step size of 0.5°, resulting with 141 rows. Applying this insight to reward function analysis, the researchers at UC Berkeley and DeepMind developed methods to compare reward functions directly, without training a policy. There are two conditions for the simulation to stop: first is if all the NRMSE of all trained speed falls under the defined PI criterion, and second is if all the trained speed converges into one final value of NRMSE for at least after 10 further iterations. The average performance of our proposed method was 0.73 of NRMSE or was 1.59° if converted to average RMSE. The mathematical descriptions of this multiple reward mechanism are expressed in Equation (6), where βt=ct2 and ∑t=1nβt=1. The loss of this function such as in the case of transfemoral amputation could severely restrict movements. Ask Question Asked 2 years ago. Using Natural Language for Reward Shaping in Reinforcement Learning. In this study, prosthetic knee is actuated by MR damper having non-linear characteristics such as hysteresis and dynamic response that are difficult to control. doi: 10.2306/scienceasia1513-1874.2012.38.386, Ekkachai, K., Tungpimolrut, K., and Nilkhamhang, I. To capture the respective joints coordinate, reflective markers were placed at hip, knee, and ankle joints. As shown in this figure, the fastest convergence was achieved by the fastest walking speed, which converges at around 3,300 iterations, followed by the walking speed of 3.6 km/h, which converges at around 6,700 iterations, and the latest is the slowest walking speed, which converges at around 6,900 iterations. In this study, θK and derivative of knee angle, θK., are used as states, while the command voltage, v, is used as the action. In particular, tasks involving human interaction depend on complex and user-dependent preferences. (A) Comparison of single reward mechanism and our proposed reward shaping function. (2012). The rest of this paper is organized as follows. A key shortcoming of RL is that the user must manually encode the task as a Force control of a magnetorheological damper using an elementary hysteresis model-based feedforward neural network. 21, 70–81. Section 3 presents the simulation and results. While this control has promising results, its application is limited to those who still have intact muscle function on the amputation site. The advantages of using this system are the rapid response and low power consumption, among others (Şahin et al., 2010). Improving the speed of convergence of multi-agent Q-learning for cooperative task-planning by a robot-team. An agent executes an action, at, to the system and environment. Piston velocity and acceleration are used as inputs to estimate MR damper force. Gait asymmetry of transfemoral amputees using mechanical and microprocessor-controlled prosthetic knees. Robot 30, 42–55. Neural network predictive control (NNPC) was employed as a control structure for the swing phase in the prosthetic knee (Ekkachai and Nilkhamhang, 2016). The Cobra Effect. Comparison between user adaptive, neural network predictive control (NNPC), and Q-learning control. Many studies on the prosthetic knee control algorithm have been conducted. Several studies have tried to apply machine learning algorithm to control prosthetic (Ekkachai and Nilkhamhang, 2016; Wen et al., 2017, 2019). Although it has shown potential outcome for human-prosthesis control tuning in a real time setting, the proposed algorithm is needed to tune a total 12 impedance parameters for 4 phases of walking. There are two actuated joints with a total of four degrees of freedom, where the hip joint has one rotational degree of freedom on the z-axis and two translation degrees of freedom on the x and y-axes; meanwhile, the knee joint has one rotational degree of freedom on the z-axis. Articles, Institute for Infocomm Research (A*STAR), Singapore. (A) Control structure of magnetorheological (MR) damper (Ekkachai et al., 2013). In this study, we investigated a control algorithm for a semi-active prosthetic knee based on reinforcement learning (RL). In this paper, we proposed a Lyapunov function based approach to shape the reward function which can effectively accelerate the training. On the first simulation, we compared our reward shaping function as formulated in Equations (7)–(11) to a single reward mechanism expressed in Equation (4). In Equation (6), βt is the specifically designed ratio of reward priority, n is the number of prediction horizon, and c is a constant that depends on n. In this study, n is set to 4; thus, c = 0.033 to be conveniently compared to the NNPC algorithm studied in Ekkachai and Nilkhamhang (2016) that set the prediction horizon to 4. It can be concluded from this simulation that the reward shaping function performed better over time in terms of NRMSE, compared to a single reward function. Further, s, a, α, and γ are the state, action, learning rate, and discounted rate, respectively, while subscript t denotes the time. Furthermore, our control strategy converged within our desired performance index and could adapt to several walking speeds. 27, 460–465. J. Rehabil. Quintero, D., Martin, A. E., and Gregg, R. D. (2017). We found that our proposed reward shaping function leads to better performance in terms of normalized root mean squared error and also showed a faster convergence trend compared to a conventional single reward function. I have a master's degree in Robotics and I write…. Reinforcement learning (RL) suffers from the designation in reward function and the large computational iterating steps until convergence. We compared our proposed reward function to a conventional single reward function under the same random initialization of a Q-matrix. It was proposed in Ekkachai et al. Reinforcement Learning: An Introduction. In this study, as only the control in the swing phase is discussed, the gait data used will be constrained into the swing phase only. The distance calculated using this approach can then be used to predict the outcome of using a certain reward function. Neurorobot., 26 November 2020 Since the necessity of rewards are the basis of reinforcement learning, it is important to understand how to create efficient reward systems, through a process called Reward Shaping There are many approaches to train the Q-function in this study. 7 is set from −7 to 7° per unit of time with predefined 0.05 step size, thus resulting with 281 columns. 1. Furthermore, the rollout method produces false negatives when the reward matches user preferences, but the RL algorithm fails to maximise. We trained this control algorithm to adapt to several walking speed datasets under one control policy and subsequently compared its performance with that of other control algorithms. Cambridge, MA: MIT Press. Training one Q-function for a specific case of a single walking speed is easy, while training multispeed at once under one Q-function is challenging. A common approach to reduce interaction time with the environment is to use reward shaping, which involves carefully designing reward functions that provide the agent intermediate rewards for progress towards the goal. Section 2 describes the specific MR damper system, double pendulum model as the environment, and the dataset that we used, as well as the details on Q-learning control. Based on this facts, our proposed Q-learning control can potentially be used for other structure of MR-damper or even other impedance-based machine for semi-active prosthetic. Struct. doi: 10.1016/j.gaitpost.2007.07.011, Lawson, B. E., Mitchell, J., Truex, D., Shultz, A., Ledoux, E., and Goldfarb, M. (2014). We have shown that our proposed reward function demonstrated a trend of faster convergence compared to a single reward mechanism as depicted in Figure 4A. The graphical description of this reward design is depicted in Figure 2C. The user-adaptive control as investigated in Herr and Wilkenfeld (2003) is an example of an adaptive control that applied the MR damper-based prosthetic knee. EPIC distance is defined using Pearson distance as follows: Where, D: distance, R: rewards, S: current state, A: action performed, S1 : changed state. The size of the Q-matrix depends on the number of states and actions. |,,, Creative Commons Attribution License (CC BY). The voltage is converted into F^ following Figure 1A and passed on to the double pendulum model for swing phase simulation. Moreover, in some of the walking speeds, this control structure performs better than the NNPC algorithm. Most real-world tasks have far more complex reward functions than this. Comparison between user-adaptive control (green dashed line), neural network predictive control (NNPC) (red line), and Q-learning control (black line) for different walking speeds: (A) 2.4 km/h, (B) 3.6 km/h, and (C) 5.4 km/h. 2.2 Reinforcement Learning with Reward Shaping With reward shaping, the agent is provided with additional shaping rewards that come from a deterministic function, F: S×A×S → R. However, there is no guarantee that an MDP with arbitrary reward shaping will have an optimal policy that is consistent with the original MDP. The advantages of using this control structure are that it can be trained online, and also it is a model-free control algorithm that does not require prior knowledge of the system to be controlled. This occurrence happened because a faster walking speed generally indicates a short time in the gait cycle, resulting in a less swing-phase time. The reward shaping function is preferred to follow a decayed exponential function rather than a linear function to better train the Q-function to reach the state with the largest reward value, which can lead to faster convergence. Further, δ, Lu, and Ll are the reward constants set arbitrarily to 0.01, performance limit to obtain the positive reward, and performance limit to obtain the lowest reward, respectively. Syst. 232, 309–324. Inspired by such a technique, we implement the reward shaping method in Eq. *Correspondence: Yonatan Hutabarat,, Front. θK is calculated by θK = θT − θL, where subscripts T and L denote thigh and leg segment, respectively, as shown in Figure 1B. For each learning rate, simulation was performed three times and average NRMSE for each learning rate were recorded. We then measured the moving average of NRMSE parameter with a constrained maximum iterations of 3000 and a fixed learning rate of 0.1. Success or failure in this case is determined by a certain performance index depending on the system and environment involved. Meanwhile, this existing study (Wen et al., 2019) used the RL algorithm to tune a total of 12 impedance parameters of the robotic knee; thus, the output variables are 12. doi: 10.1108/01439910310457706, Hoover, C. D., Fulk, G. D., and Fite, K. B. In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. This controller is programmed to provide a control output of the current state machine obtained from specific rules based on varying sensing information. The discounted factor is a variable that determines how the Q-function acts toward the reward. A finite state machine-based controller is often found in the powered knee (Wen et al., 2017). The structure of the reward mechanism in the Q-learning algorithm used in this study is modified into a rationed multiple rewards as a function of time. • Solu-on: Reward shaping (intermediate rewards). Potential- The general structure of RL is consisted of an agent and a system/environment. Higher learning rate, which if sets closer to 1, indicates that the Q-function is updated quickly per iteration, while the Q-function is never be updated if it is set to 0. Swing phase control of semi-active prosthetic knee using neural network predictive control with particle swarm optimization. IEEE Int. Shaping rewards is hard. Sci. As Q-learning is following an off-policy method, actions were selected based on the maximum value of the Q-function on the current states, maxQ(s1(t), s2(t)). A robotic leg prosthesis: design, control, and implementation. Markov decision processes. (2016). Belief Reward Shaping in Reinforcement Learning Ofir Marom1, Benjamin Rosman 1 , 2 1University of the Witwatersrand, Johannesburg, South Africa 2Council for Scientific and Industrial Research, Pretoria, South Africa Abstract A key challenge in many reinforcement learning problems is delayed rewards, which can significantly slow down learning. Reward design decides the robustness of an RL system. Here, one FNN coupled with EHM acted as a hysteresis model, and the output of this network was fed to the other FNN that acted as the gain function. WK contributed to study conception and design, provided critical review, and supervised the overall study. A high-speed camera was used to capture joints coordinate and later converted to relative joint angles. As the controller aims to mimic the biological knee trajectory in the swing phase, the reward will be given according to whether the prosthetic knee can follow the biological knee trajectory. To capture these behaviors of MR damper, the elementary hysteresis model (EHM) based feed-forward neural network (FNN) model is used in our simulation. Neurorobot. 2015, 410–415. (2007). (1991). Since we proposed a RL-based algorithm, all the recorded knee angle data with a total of 200 sets per walking speed will be used. Gait and balance of transfemoral amputees using passive mechanical and microprocessor-controlled prosthetic knees. How to accelerate the training process in RL plays a vital role. 50, 273–314. A new powered lower limb prosthesis control framework based on adaptive dynamic programming. Potential-based reward shaping has been successfully ap-plied in such complex domains as RoboCup KeepAway soccer [4] and StarCraft [5], improving agent performance significantly. Those two learning rates did also not show any significant performance changes over the constrained iteration. (C) Comparison of cumulative reward over iteration by each of the simulated learning rates. 19:035012. doi: 10.1088/0964-1726/19/3/035012, Sawers, A. Figure 6. (B) Effect of various learning rates to the overall performance (normalized root mean squared error, NRMSE). 2.1 Difference Rewards To use reinforcement learning in a multiagent system, it is important to reward an agent based on its contribution to the system. Overall, Q-learning method perform within 1% of NRMSE, which followed the designed common reward function for different walking speed. The Q-learning control comprised a Q-function that stores its value in a Q-matrix and a reward function following the reward shaping function proposed in this study. IEEE Robot. In this study, PI is aimed to be within 0.01, indicating that the error should be under 1%. doi: 10.1109/MRA.2014.2360303. Potential-based reward shaping in DQN reinforcement learning. Unfortunately, this method is computationally expensive because it requires us to solve an RL problem. The proposed controller was designed with the structure of a tabular reinforcement Q-learning algorithm, a subset in machine learning algorithms. YH contributed to algorithm design and development, data analysis and interpretation, and writing the first draft. Figure 5. MR damper is defined as the system, that is, the main actuator to be controlled. Recent reinforcement learning (RL) approaches have shown strong performance in complex domains such as Atari games, but are often highly sample inefficient. View all In this simulation, the structure of the Q-matrix is a three-dimensional matrix consisting of l rows of state θK(t), m columns of state θK(t)., and n layers of action v. Q-matrix must cover all the states and actions available on the system. of reward shaping, previously studied separately, are di er-ence rewards and potential-based reward shaping. 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Evaluation of function, performance, and preference as transfemoral amputees transition from mechanical to microprocessor control of the prosthetic knee. One type of reward that always generates a low reward horizon is opportunity value. There are two steps in the process of transfer learning: extracting knowledge from previously learned tasks and transferring that … This work introduces novel ways of evaluating reward functions for reinforcement learning tasks. The drawbacks of reinforcement learning include long convergence time, enormous training data size, and difficult reproduction. 26, 489–493. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. In this study, we investigated a model-free Q-learning control algorithm with a reward shaping function as the swing phase control in the MR damper-based prosthetic knee. However, sparse rewards also slow down learning because the agent needs to take many actions before getting any reward. In this manner, the proposed controller performance can be compared to the previous method with same dataset. LetF be the shaping function, thenR + F is the new reward. Although we cannot provide detailed comparison of our proposed method with another RL-based method in Wen et al. The comparison of 2.4, 3.6, and 5.4 km/h walking speed are depicted in Figure 6 and Table 1. A variable reward as a function of PI associating a decayed function, which is proposed as a reward function herein, has led to a better reward mechanism. A novel approach to model magneto-rheological dampers using EHM with a feed-forward neural network. This is understandable since it was applied to powered prosthetic knee (Wen et al., 2019). By providing rewards that are more informative and more immediate, even though approximate, shaping may help (B) βt as an exponential function with n = 4. 26, 305–312. Introduction. Putnam, C. A. Dev. doi: 10.1109/TCYB.2019.2890974, Wen, Y., Si, J., Gao, X., Huang, S., and Huang, H. H. (2017). MH provided critical review and contributed additional texts to the draft. Conf. Reinforcement learning (RL) has enjoyed much recent suc- cess in domains ranging from game-playing to real robotics tasks. (B) Double pendulum model to simulate swing phase with MR damper attachment with distance dMR from the knee joint. This raises a need of online learning model that could adapt if users change walking pattern due to weight change or using different costume. The design and initial experimental validation of an active myoelectric transfemoral prosthesis. The reward function is also designed to have a continuous value over a specified boundary and follow a decaying exponential function. Abstract: Potential-based reward shaping (PBRS) is a particular category of machine learning methods which aims to improve the learning speed of a reinforcement learning agent by extracting and utilizing extra knowledge while performing a task. Eng. Technol. Motivation Approximating Q-functions Shaping Rewards and Initial Q-Functions Conclusion Reinforcement Learning – Some Weaknesses In the previous lectures, we looked at fundamental temporal difference (TD) methods for reinforcement learning. doi: 10.1109/TCST.2016.2643566, Sadhu, A. K., and Konar, A. Lett. Although there has not been a detailed study about the acceptable criterion in terms of the NRMSE performance index of the knee trajectory in a prosthetic knee, this study aims to mimic the biological knee trajectory, which is shown by PI. The best training process of this simulation over a total of 10 training processes is depicted in Figure 5. – Add rewards/penal-es for achieving sub-goals/errors: • subgoal: grasped-puck A key feature of Reinforcement Learning is the use of a reward signal. No use, distribution or reproduction is permitted which does not comply with these terms. Here, the proposed Q-learning control is discussed. The effect of these learning rate to NRMSE is shown in Figures 4B,C. Plan-based reward shaping for reinforcement learning Abstract: Reinforcement learning, while being a highly popular learning technique for agents and multi-agent systems, has so far encountered difficulties when applying it to more complex domains due to scaling-up problems. Furthermore, EMG-based control has been investigated in several studies, such as in Hoover et al. performs reward shaping. Impact Factor 2.574 | CiteScore 4.6More on impact ›, Advanced Planning, Control, and Signal Processing Methods and Applications in Robotic Systems (2013). reinforcement-learning-based AI systems become more general and autonomous, the design of reward mechanisms that elicit desired behaviours becomes both more important and more difficult. IEEE Trans. On the right column, the policy has been trained through reinforcement learning and reward shaping, such that the shaping potential is a generative model that describes the demonstration data. Pearson distance between two random variables X and Y is calculated as follows: Where ρ(X, Y ) is the Pearson correlation between X and Y . In terms of cost function, knee trajectory is only one of the parameters to be optimized among other correlated systems, such as ankle and foot prostheses, to achieve better gait symmetry and reduce metabolic costs. The reward function was designed as a function of the performance index that accounts for the trajectory of the subject-specific knee angle. Second, this study proposed a tabular-discretized Q-function stored in a Q-matrix. Magnetorheological (MR) damper is one of the examples that utilize this function by manipulating the strength of the magnetic field, which is applied to magnetic particles in a carrier fluid. Further, the reward priority given at the specified prediction horizon is an exponential function, as depicted in Figure 2B. 22:5030. doi: 10.1088/0964-1726/22/11/115030, Fernandez-Gauna, B., Marques, I., and Graña, M. (2013). We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the cost-to-go oracle shortens the learner’s planning horizon as function of its accuracy: a Thus, the update rule of the Q-function can be written as in Equation (5). In this study, we investigated our proposed control algorithm for the swing phase controller in the MR-damper-based prosthetic knee. In this study, the agent is the Q-function with a mathematical description, as shown in Equation (4). (2019), the swing phase was divided into swing flexion and swing extension where the ADP tuner would tune the impedance parameters accordingly with respect to each state. Recent reinforcement learning (RL) approaches have shown strong performance in complex domains such as Atari games, but are often highly sample inefficient. The MR damper is attached at a distance, dMR, away from the knee joint. Online reinforcement learning control for the personalization of a robotic knee prosthesis. Note that δ, Lu, Ll, Rmax, and Rmin can be defined accordingly for other applications depending on the system being evaluated.