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Animals have exquisite control of their bodies, allowing them to perform a diverse range of behaviours. How such control is implemented by the brain, however, remains unclear. Advancing our understanding requires models that can relate principles of control to the structure of neural activity in behaving animals. Here, to facilitate this, we built a ‘virtual rodent’, in which an artificial neural network actuates a biomechanically realistic model of the rat 1 in a physics simulator 2 . We used deep reinforcement learning 3 , 4 – 5 to train the virtual agent to imitate the behaviour of freely moving rats, thus allowing us to compare neural activity recorded in real rats to the network activity of a virtual rodent mimicking their behaviour. We found that neural activity in the sensorimotor striatum and motor cortex was better predicted by the virtual rodent’s network activity than by any features of the real rat’s movements, consistent with both regions implementing inverse dynamics 6 . Furthermore, the network’s latent variability predicted the structure of neural variability across behaviours and afforded robustness in a way consistent with the minimal intervention principle of optimal feedback control 7 . These results demonstrate how physical simulation of biomechanically realistic virtual animals can help interpret the structure of neural activity across behaviour and relate it to theoretical principles of motor control. We built an artificial neural network to control a biomechanically realistic virtual rodent, which, when trained to imitate real rats, predicts neural activity and variability across natural behaviours.

We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a derivative-free approach to form these convex approximations by computing samples of the dynamics, cost, and constraint functions and letting the solver interpolate between them. Our framework includes sample-based trajectory optimization techniques like model-predictive path integral (MPPI) control as a special case and generalizes them to enable features like multiple shooting and general equality and inequality constraints that are traditionally associated with derivative-based sequential convex programming methods. The resulting framework is simple, flexible, and capable of solving a wide variety of practical motion planning and control problems.

We introduce a novel musculoskeletal model of a dog, procedurally generated from accurate 3D muscle meshes. Accompanying this model is a motion capture-based locomotion task compatible with a variety of control algorithms, as well as an improved muscle dynamics model designed to enhance convergence in differentiable control frameworks. We validate our approach by comparing simulated muscle activation patterns with experimentally obtained electromyography (EMG) data from previous canine locomotion studies. This work aims to bridge gaps between biomechanics, robotics, and computational neuroscience, offering a robust platform for researchers investigating muscle actuation and neuromuscular control.We plan to release the full model along with the retargeted motion capture clips to facilitate further research and development.

We demonstrate the surprising real-world effectiveness of a very simple approach to whole-body model-predictive control (MPC) of quadruped and humanoid robots: the iterative LQR (iLQR) algorithm with MuJoCo dynamics and finite-difference approximated derivatives. Building upon the previous success of model-based behavior synthesis and control of locomotion and manipulation tasks with MuJoCo in simulation, we show that these policies can easily generalize to the real world with few sim-to-real considerations. Our baseline method achieves real-time whole-body MPC on a variety of hardware experiments, including dynamic quadruped locomotion, quadruped walking on two legs, and full-sized humanoid bipedal locomotion. We hope this easy-to-reproduce hardware baseline lowers the barrier to entry for real-world whole-body MPC research and contributes to accelerating research velocity in the community. Our code and experiment videos will be available online at:https://johnzhang3.github.io/mujoco_ilqr

We demonstrate the surprising real-world effectiveness of a very simple approach to whole-body model-predictive control (MPC) of quadruped and humanoid robots: the iterative LQR (iLQR) algorithm with MuJoCo dynamics and finite-difference approximated derivatives. Building upon the previous success of model-based behavior synthesis and control of locomotion and manipulation tasks with MuJoCo in simulation, we show that these policies can easily generalize to the real world with few sim-to-real considerations. Our baseline method achieves real-time whole-body MPC on a variety of hardware experiments, including dynamic quadruped locomotion, quadruped walking on two legs, and full-sized humanoid bipedal locomotion. We hope this easy-to-reproduce hardware baseline lowers the barrier to entry for real-world whole-body MPC research and contributes to accelerating research velocity in the community. Our code and experiment videos will be available online at:https://johnzhang3.github.io/mujoco_ilqr

We investigate whether Deep Reinforcement Learning (Deep RL) is able to synthesize sophisticated and safe movement skills for a low-cost, miniature humanoid robot that can be composed into complex behavioral strategies in dynamic environments. We used Deep RL to train a humanoid robot with 20 actuated joints to play a simplified one-versus-one (1v1) soccer game. The resulting agent exhibits robust and dynamic movement skills such as rapid fall recovery, walking, turning, kicking and more; and it transitions between them in a smooth, stable, and efficient manner. The agent's locomotion and tactical behavior adapts to specific game contexts in a way that would be impractical to manually design. The agent also developed a basic strategic understanding of the game, and learned, for instance, to anticipate ball movements and to block opponent shots. Our agent was trained in simulation and transferred to real robots zero-shot. We found that a combination of sufficiently high-frequency control, targeted dynamics randomization, and perturbations during training in simulation enabled good-quality transfer. Although the robots are inherently fragile, basic regularization of the behavior during training led the robots to learn safe and effective movements while still performing in a dynamic and agile way -- well beyond what is intuitively expected from the robot. Indeed, in experiments, they walked 181% faster, turned 302% faster, took 63% less time to get up, and kicked a ball 34% faster than a scripted baseline, while efficiently combining the skills to achieve the longer term objectives.

Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static contact force model instead of a full simulator. Using a feature vector that contains information about the configuration and control, we find a linear mapping adequately captures the relationship between this feature vector and the sensed contact forces. A novel Linear Model Learning (LML) algorithm is used to solve for the globally optimal mapping in real time without any matrix inversions, resulting in an algorithm that runs in nearly constant time on a GPU as the model size increases. We validate the proposed approach for connector insertion both in simulation and hardware experiments, where the learned model is combined with an optimization-based controller to achieve smooth insertions in the presence of misalignments and uncertainty. Our website featuring videos, code, and more materials is available at https://model-based-plugging.github.io/.

We introduce MuJoCo Playground, a fully open-source framework for robot learning built with MJX, with the express goal of streamlining simulation, training, and sim-to-real transfer onto robots. With a simple \"pip install playground\", researchers can train policies in minutes on a single GPU. Playground supports diverse robotic platforms, including quadrupeds, humanoids, dexterous hands, and robotic arms, enabling zero-shot sim-to-real transfer from both state and pixel inputs. This is achieved through an integrated stack comprising a physics engine, batch renderer, and training environments. Along with video results, the entire framework is freely available at playground.mujoco.org

We introduce MuJoCo MPC (MJPC), an open-source, interactive application and software framework for real-time predictive control, based on MuJoCo physics. MJPC allows the user to easily author and solve complex robotics tasks, and currently supports three shooting-based planners: derivative-based iLQG and Gradient Descent, and a simple derivative-free method we call Predictive Sampling. Predictive Sampling was designed as an elementary baseline, mostly for its pedagogical value, but turned out to be surprisingly competitive with the more established algorithms. This work does not present algorithmic advances, and instead, prioritises performant algorithms, simple code, and accessibility of model-based methods via intuitive and interactive software. MJPC is available at: github.com/deepmind/mujoco_mpc, a video summary can be viewed at: dpmd.ai/mjpc.

Muscle-actuated control is a research topic that spans multiple domains, including biomechanics, neuroscience, reinforcement learning, robotics, and graphics. This type of control is particularly challenging as bodies are often overactuated and dynamics are delayed and non-linear. It is however a very well tested and tuned actuation mechanism that has undergone millions of years of evolution with interesting properties exploiting passive forces and efficient energy storage of muscle-tendon units. To facilitate research on muscle-actuated simulation, we release a 3D musculoskeletal simulation of an ostrich based on the MuJoCo physics engine. The ostrich is one of the fastest bipeds on earth and therefore makes an excellent model for studying muscle-actuated bipedal locomotion. The model is based on CT scans and dissections used to collect actual muscle data, such as insertion sites, lengths, and pennation angles. Along with this model, we also provide a set of reinforcement learning tasks, including reference motion tracking, running, and neck control, used to infer muscle actuation patterns. The reference motion data is based on motion capture clips of various behaviors that we preprocessed and adapted to our model. This paper describes how the model was built and iteratively improved using the tasks. We also evaluate the accuracy of the muscle actuation patterns by comparing them to experimentally collected electromyographic data from locomoting birds. The results demonstrate the need for rich reward signals or regularization techniques to constrain muscle excitations and produce realistic movements. Overall, we believe that this work can provide a useful bridge between fields of research interested in muscle actuation.