1 Introduction
The ability to learn through experience is a hallmark of intelligence. Humans most certainly learn this way, and, using reinforcement learning (RL) [Sutton and Barto1998], autonomous agents may do so as well. However, learning to perform a task based solely on one’s own experience can be very difficult and slow. Humans are often able to learn much faster by observing and imitating the behavior of others. Enabling this same ability in autonomous agents, referred to as learning from demonstration (LfD), has been given a great deal of attention in the research community [Schaal1997, Argall et al.2009].
While much of LfD research is motivated by the way humans learn from observing others, it has largely overlooked the integration of two important aspects of that paradigm. First, unlike the classical LfD setting, humans do not typically have knowledge of the precise actions executed by demonstrators, i.e., the internal control signals demonstrators use to guide their behavior Second, humans are able to perform imitation without needing to spend a lot of time interacting with their environment after the demonstration has been provided.
Most LfD work is unlike human imitation in its assumption that imitators know the actions executed by demonstrators. Human imitators typically do not have access to this information, and requiring it immediately precludes using a large amount of demonstration data where action sequences are not given. For example, there is a great number of tutorial videos on YouTube that only provide the observer knowledge of the demonstrator’s state trajectory. It would be immensely beneficial if we could devise LfD algorithms to make use of such information.
Another challenge faced by LfD is the necessity of environment interaction, which can be expensive in several regards. One is the amount of time it requires: executing actions, either in the real world or in simulation, takes time. If a learning algorithm requires that a large number of actions must be executed in order to find a good imitation policy after a demonstration is presented, then there will be an undesirable amount of delay before the imitating agent will be successful. Furthermore, algorithms that require postdemonstration interaction typically require it again and again for each newlydemonstrated task, which could result in even more delay. Beyond delay, environment interaction can also be risky. For example, when training autonomous vehicles, operating on city streets while learning might endanger lives or lead to costly damage due to crashes. Therefore, we desire an algorithm for which environment interactions can be performed as a preprocessing step  perhaps in a safer environment  and where the information learned from those interactions can be reused for a variety of demonstrated tasks.
In this paper, we propose a new imitation learning algorithm called behavioral cloning from observation (BCO). BCO simultaneously addresses both of the issues discussed above, i.e., it provides reasonable imitation policies almost immediately upon observing statetrajectoryonly demonstrations. First, it calls for the agent to learn a taskindependent, inverse dynamics model in a predemonstration, exploratory phase. Then, upon observation of a demonstration without action information, BCO uses the learned model to infer the missing actions. Finally, BCO uses the demonstration and the inferred actions to find a policy via behavioral cloning. If postdemonstration environment interaction is allowed, BCO additionally specifies an iterative scheme where the agent uses the extra interaction time in order to learn a better model and improve its imitation policy. This iterative scheme therefore provides a tradeoff between imitation performance and postdemonstration environment interaction.
2 Related Work
BCO is related to both imitation learning and modelbased learning. We begin with a review of imitation learning approaches, which typically fall under one of two broad categories: behavioral cloning (BC) and inverse reinforcement learning (IRL).
Behavioral cloning [Bain and Sommut1999, Ross et al.2011, Daftry et al.2016]
is one of the main methods to approach an imitation learning problem. The agent receives as training data both the encountered states and actions of the demonstrator, and then uses a classifier or regressor to replicate the expert’s policy
[Ross and Bagnell2010]. This method is powerful in the sense that it is capable of imitating the demonstrator immediately without having to interact with the environment. Accordingly, BC has been used in a variety of applications. For instance, it has been used to train a quadrotor to fly down a forest trail [Giusti et al.2016]. There, the training data is the pictures of the forest trail labeled with the actions that the demonstrating quadrotor used, and the policy is modeled as a convolutional neural network classifier. In the end, the quadrotor manages to fly down the trail successfully. BC has also been used in autonomous driving
[Bojarski et al.2016]. The training data is acquired from a human demonstrator, and a convolutional neural network is trained to map raw pixels from a single frontfacing camera directly to steering commands. After training, the vehicle is capable of driving in traffic on local roads. BC has also been successfully used to teach manipulator robots complex, multistep, realworld tasks using kinesthetic demonstration [Niekum et al.2015]. While behavioral cloning is powerful, it is also only applicable in scenarios where the demonstrator’s action sequences are available. However, when humans want to imitate each other’s actions, they do not have access to the internal control signals the demonstrator used. Instead, they only see the effects of those actions. In our setting, we wish to perform imitation in these scenarios, and so we cannot apply BC techniques as they are typically formulated.Inverse reinforcement learning is a second category of imitation learning. IRL techniques seek to learn a cost function that has the minimum value for the demonstrated actions. The learned cost function is then used in combination with RL methods to find an imitation policy. Like BC techniques, IRL methods usually assume that stateaction pairs are available [Finn et al.2016, Ho and Ermon2016, Ho et al.2016], and also that the reward is a function of both states and actions. An exception is the work of Liu et al. [2017]. In this work, it is assumed that both demonstrator and imitator are capable of following a trajectory at the exact same pace to perform a task, and the IRL method defines the reward signal to be the proximity of the imitator and demonstrator’s encoded state features at each time step. As a result, the reward signal can only be generated after the demonstration is made available, after which reinforcement learning and environment interaction must be completed in order to find a good policy. In our work, we wish to minimize the amount of environment interaction necessary after the demonstration is provided, and so we seek an alternative to IRL.
BCO is also related to the modelbased learning literature in that it makes use of learned models of the environment. In general, modelbased methods have major advantages over those that are modelfree. First, they are more sampleefficient [Chebotar et al.2017], i.e., they do not require as many environment interactions as modelfree methods. Second, the learned models can be transferred across tasks [Taylor et al.2008]
. Typical modellearning techniques focus on obtaining an estimate of the transition dynamics model, i.e., a mapping from current state and action to the next state. In our work, on the other hand, we want the agent to learn a model of the environment that will help us infer missing actions, and therefore BCO learns a slightlydifferent inverse dynamics model, i.e., a mapping from state transitions to the actions
[Hanna and Stone2017].There has also been recent work done where inverse models have been used to perform imitation learning in the absence of action information. Niekum et al [2015a] present such a technique for situations in which the kinematic equations are known. Nair et al [2017] propose a technique that first learns an inverse dynamics model and then use that model to estimate the missing action information at each time step from a single demonstration. The method we develop here, on the other hand, both does not assume prior knowledge of the inverse model and is capable of generalizing in cases when mulitiple demonstrations are available.
3 Problem Formulation
We consider agents acting within the broad framework of Markov decision processes (MDPs). We denote a MDP using the 5tuple
, where is the agent’s state space, is its action space,is a function denoting the probability of the agent transitioning from state
to after taking action , is a function specifying the immediate reward that the agent receives for taking a specific action in a given state, and is a discount factor. In this framework, agent behavior can be specified by a policy, , which specifies the action (or distribution over actions) that the agent should use when in a particular state. We denote the set of state transitions experienced by an agent during a particular execution of a policy by .In the context of these transitions, we will be interested in the inverse dynamics model, , which is the probability of having taken action given that the agent transitioned from state to . Moreover, we specifically seek taskindependent models. We assume that some of the state features are specifically related to the task and others specifically to the agent, i.e., a given state can be partitioned into an agentspecific state, , and a taskspecific state, , which are members of sets and , respectively (i.e., ) [Konidaris2006, Gupta et al.2017]. Using this partitioning, we define the agentspecific inverse dynamics model to be a function that maps a pair of agentspecific state transitions, , to a distribution of agent actions that is likely to have given rise to that transition.
Imitation learning is typically defined in the context of a MDP without an explicitlydefined reward function, i.e., . The learning problem is for an agent to determine an imitation policy, that the agent may use in order to behave like the expert, using a provided set of expert demonstrations in which each is a demonstrated stateaction trajectory . Therefore, in this setting, the agent must have access to the demonstrator’s actions. If the imitator is unable to observe the action sequences used by the demonstrator, the resulting imitation learning problem has recently been referred to as imitation from observation [Liu et al.2017]. In this setting, one seeks to find an imitation policy from a set of stateonly demonstrations in which each is a stateonly trajectory .
The specific problem that we are interested in is imitation from observation under a constrained number of environment interactions. By environment interactions we mean time steps for which we require our agent to gather new data by executing an action in its environment and observing the state outcome. We are concerned here in particular with the cost of the learning process, in terms of the number of environment interactions, both before and after the expert demonstrations are provided. Pre and postdemonstration environment interactions are represented by and , respectively, to denote sets of interactions that must be executed by a learner before and after a demonstration becomes available. In this context, we are concerned here with the following specific goal: given a set of stateonly demonstration trajectories, , find a good imitation policy using a minimal number of postdemonstration environment interactions, i.e., .
In pursuit of this goal, we propose a new algorithm for imitation learning that can operate both in the absence of demonstrator action information and while requiring no or very few postdemonstration environment interactions. Our framework consists of two components, each of which considers a separate part of this problem. The first of these components considers the problem of learning an agentspecific inverse dynamics model, and the second one considers the problem of learning an imitation policy from a set of demonstration trajectories.
4 Behavioral Cloning from Observation
We now describe our imitation learning algorithm, BCO, which combines inverse dynamics model learning with learning an imitation policy. We are motivated by the fact that humans have access to a large amount of prior experience about themselves, and so we aim to also provide an autonomous agent with this same prior knowledge. To do so, before any demonstration information is observed, we allow the agent to learn its own agentspecific inverse dynamics model. Then, given stateonly demonstration information, we use this learned model to infer the expert’s missing action information. Once these actions have been inferred, the agent performs imitation learning via a modified version of behavioral cloning (Figure 1). The pseudocode of the algorithm is given in Algorithm 1.
4.1 Inverse Dynamics Model Learning
In order to infer missing action information, we first allow the agent to acquire prior experience in the form of an agentspecific inverse dynamics model. In order to do so, we let the agent perform an exploration policy, . In this work, we let be a random policy (Algorithm 1, Line 2). While executing this policy, the agent performs some number of interactions with the environment, i.e., . Because we seek an agentspecific inverse dynamics model as described in Section 3, we extract the agentspecific part of the states in and store them as , and their associated actions, (Algorithm 1, Lines 58). Given this information, the problem of learning an agentspecific inverse dynamics model is that of finding the parameter for which best describes the observed transitions. We formulate this problem as one of maximumlikelihood estimation, i.e., we seek as
(1) 
where is the conditional distribution over actions induced by
given a specific state transition. Any number of supervised learning techniques, denoted as “modelLearning” in Algorithm
1, may be used to solve (1).Some details regarding particular choices made in this paper: For domains with a continuous action space, we assume a Gaussian distribution over each action dimension and our model estimates the individual means and standard deviations. We use a neural network for
, where the network receives a state transition as input and outputs the mean for each action dimension. The standard deviation is also learned for each dimension, but it is computed independently of the state transitions. In order to train this network (i.e., to find in (1)), we use the Adam variant [Kingma and Ba2014] of stochastic gradient decent. Intuitively, the gradient for each sample is computed by finding a change in that would increase the probability of with respect to the distribution specified by . When the action space is discrete, we again use a neural network for , where the network computes the probability of taking each action via a softmax function.4.2 Behavioral Cloning
Our overarching problem is that of finding a good imitation policy from a set of stateonly demonstration trajectories, where each is a trajectory . Note that, although the inverse dynamics model is learned using a set of agentgenerated data in Section 4.1, the data used there is not utilized in this step. In order to use the learned agentspecific inverse dynamics model, we first extract the agentspecific part of the demonstrated state sequences and then form the set of demonstrated agentspecific state transitions (Algorithm 1, Line 10). Next, for each transition , the algorithm computes the modelpredicted distribution over demonstrator actions, and uses the maximumlikelihood action as the inferred action, , which is placed in a set (Algorithm 1, Line 11). Using these inferred actions, we then build the set of complete stateaction pairs .
With this new set of stateaction pairs, we may now seek the imitation policy . We cast this problem as one of behavioral cloning, i.e., given a set of stateaction tuples , the problem of learning an imitation policy becomes that of finding the parameter for which best matches this set of provided stateaction pairs (Algorithm 1, Line 12). We find this parameter using maximumlikelihood estimation, i.e., we seek as
(2) 
Some details regarding particular choices made in this paper: For continuous action spaces, we assume our policy to be Gaussian over each action dimension, and, for discrete actions spaces we use a softmax function to represent the probability of selecting each value. We let be a neural network that receives as input a state and outputs either the Gaussian distribution parameters or the action probabilities for continuous or discrete action spaces, respectively. We then solve for in (2) using Adam SGD, where the intuitive view of the gradient is that it seeks to find changes in that increase the probability of each inferred demonstrator action, , in the imitation policy’s distribution .
4.3 Model Improvement
The techniques described above form the building blocks of BCO. If one is willing to tolerate postdemonstration environment interaction, a modified version of our algorithm can further improve both the learned model and the resulting imitation policy. This modified algorithm proceeds as follows. After the behavioral cloning step, the agent executes the imitation policy in the environment for a short period of time. Then, the newlyobserved stateaction sequences are used to update the model, and, accordingly, the imitation policy itself. The above procedure is repeated until there is no more improvement in the imitation policy. We call this modified version of our algorithm BCO(), where is a userspecified parameter that is used to control the number of postdemonstration environment interactions at each iteration, , according to . The total number of postdemonstration interactions required by BCO() can be calculated as , where is the total number of modelimprovement iterations required by BCO(). Using a nonzero , the model is able to leverage postdemonstration environment interaction in order to more accurately estimate the actions taken by the demonstrator, and therefore improve its learned imitation policy. If one has a fixed budget for postdemonstration interactions, one could consider terminating the modelimprovement iterations early, i.e., specify both and .
5 Implementation and Experimental Results
We evaluated BCO() in several domains available in OpenAI Gym [Brockman et al.2016]. Continuous tasks are simulated by MuJoCo [Todorov et al.2012]. These domains have different levels of difficulty, as measured by the complexity of the dynamics and the size and continuity of the state and action spaces. Ordered from easy to hard, the domains we considered are: CartPole, MountainCar, Reacher, and Antv1. Each of these domains has predefined state features, actions and reward functions in the simulator. Any RL algorithm could be used with this reward function to generate an expert policy. Since trust region policy optimization (TRPO) [Schulman et al.2015] has shown promising performance in simulation [Liu et al.2017], we generated our demonstrations using agents trained with this method.
We evaluated our algorithm in two senses. First, with respect to the number of environment interactions required to attain a certain performance. In a realworld environment, interactions can be expensive which makes it a very important criterion. The second way in which we evaluate our algorithm is with respect to data efficiency, i.e., the imitator’s task performance as a function of the amount of available demonstration data. In general, demonstration data is scarce, and so making the best use of it is very important.
We compared BCO() to the following methods:

Behavioral Cloning (BC): This method applies supervised learning over stateaction pairs provided by the demonstrator.

Feature Expectation Matching (FEM) [Ho et al.2016]: A modified version of the approach presented by Abbeel and Ng [2004]. It uses trust region policy optimization with a linear cost function in order to train train neural network policies.

General Adversarial Imitation Learning (GAIL) [Ho and Ermon2016]: A stateoftheart in IRL. It uses a specific class of cost functions which allows for the use of generative adversarial networks in order to do apprenticeship learning.
Note in particular that our method is the only method that does not have access to the demonstrator’s actions. However, as our results will show, BCO() can still achieve comparable performance to these other techniques, and do so while requiring far fewer environment interactions.
5.1 Training Details and Results
Because both BC and BCO() rely on supervised learning methods, we use only 70% of the available data for training and use the rest for validation. We stop training when the error on the 30% validation data starts to increase. For the other methods, all available data was used in the training process. We will now discuss the architecture, details for each domain.

CartPole: The goal is to keep the pole vertically upward as long as possible (Figure 2(a)). This domain has a discrete action space. In this domain, we considered linear models over the predefined state features for both the inverse dynamics model and the imitation policy and we only used interactions to learn the dynamics.

MountainCar: The goal is to have the car reach the target point (Figure 2(b)). This domain has a discrete action space. In this domain, the data set for learning the inverse dynamics model is acquired by letting the agent to explore its action space for
time steps. For both the imitation policy and inverse dynamics model, we used neural networks with two hidden layers, 8 nodes each, and leaky rectified linear activation functions (LReLU).

Reacher: This domain has a continuous action space. The goal is to have the fingertip of the arm reach the target point whose position changes in every episode (Figure 2(c)). Therefore, in this domain, we can partition the statespace to agentspecific features (i.e., those only related to the arm) and taskspecific features (i.e., those related to the position of the target). A neural network architecture with two hidden layers of 100 LReLU nodes are used with agentspecific state transitionaction pairs in order to learn the dynamics and then this model is used to learn a policy which also has two layers but with 32 LReLU nodes.

Ant: The goal to have the ant to run as fast as possible(Figure 2(d)). This domain has a continuous action space. This is the most complex domain considered in this work. The state and action space are 111 and 8 dimensional, respectively. The number of interactions needed to learn the dynamics was and the architectures for inverse dynamics learning and the policy are similar to those we used in Reacher.
5.2 Discussion
Each experiment was executed twenty times, and all results presented here are the average values over these twenty runs. We selected twenty trials because we empirically observed very small standard error bars in our results. This is likely a reflection of the relatively low variance in the expert demonstrations.
In our first experiment, we compare the number of environment interactions needed for BCO(0) with the number required by other methods (Figure 4.) We can clearly see how imitation performance improves as the agent is able to interact more with the environment. In the case of BCO(0), the interactions with the environment happen before the policylearning process starts, and so we represent its performance with a horizontal line. The height of the line indicates the performance, and we display the number of predemonstration environment interactions it required next to it. The random and expert policies also do not benefit from postdemonstration environment interaction, and so they are also shown using horizontal lines. From these plots, we can see that it takes at least 40 times more interactions required by GAIL or FEM to gain the same performance as BCO(0).
MountainCar (predemo )  Reacher (predemo )  Ant (predemo )  
Now, we aim to compare the performance of our algorithm BCO() with the other algorithms. To do so, we use each algorithm to train the agents, and then calculate the final performance by computing the average return over episodes. For comparison purposes, we scale these performance values such that the performance of the expert and a random policy are and , respectively. This comparison is shown in Figures 5, and 6 where we have plotted the performance of each algorithm with respect to the number of available demonstrated trajectories. Figure 5 shows the comparison between the performance of BCO(0) with all the other methods, and Figure 6 compares the performance of BCO() across different values of . In Figure 5, we can see that performance of our method is comparable with other methods even though our method is the only one without access to the actions. In the case of Reacher, the transferability of the learned inverse model is highlighted by the high performance of BCO. In the case of the Reacher and Ant domains, we can see that FEM performs poorly compared to others, perhaps because the rewards are not simple enough to be approximated by linear functions. In the CartPole domain, each of the methods performs as well as the expert and so all the lines are over each other. In the case of MountainCar, our performance is worse than other methods. Conversely, for Reacher, ours is more sample efficient than GAIL, i.e., with smaller number of demonstrations we get much better results. In the case of Ant, our method performs almost as good as GAIL. In Figure 6, we can see that BCO’s performance improves with larger since the extra environment interactions allow it to make better estimates of the demonstrator’s actions.
6 Conclusions
In this paper, we have presented BCO, an algorithm for performing imitation learning that requires neither access to demonstrator actions nor postdemonstration environment interaction. Our experimental results show that the resulting imitation policies perform favorably compared to those generated by existing imitation learning approaches that do require access to demonstrator actions. Moreover, BCO requires fewer postdemonstration environment interactions than these other techniques, meaning that a reasonable imitation policy can be executed with less delay.
Acknowledgments
Peter Stone serves on the Board of Directors of Cogitai, Inc. The terms of this arrangement have been reviewed and approved by the University of Texas at Austin in accordance with its policy on objectivity in research.
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