{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "todorov-erez-tassa-mujoco-control-physics-engine-2012", "title": "MuJoCo: a physics engine designed for control optimization", "summary": "Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit.", "boundary": "Contact formulations involve different approximations and optimization trade-offs. The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. Later ownership, Python suites, differentiable engines and licensing changes are not attributed retroactively to the original three-author contribution.", "area": "Robotics simulation and numerical control tools", "topic": "Artificial intelligence", "year": 2012, "lane": "HUMAN", "result": "ALGORITHM", "package_id": "todorov-erez-tassa-mujoco-control-physics-engine-2012", "target": { "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "content_hash": "sha256:f5fbefe0c5beb115d5200f0266844381ba15b66f61cfe182d75f79c378660e33" }, "humans": [ "Emanuel Todorov", "Tom Erez", "Yuval Tassa" ], "authors_complete": true, "human_role_note": "Source-listed human researchers and engineers for the exact method or resource. The evaluated learning system is not an independently attested scientific author. Earlier methods, funding and data-collection roles remain separate. 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MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit.", "scope": "Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit. Contact formulations involve different approximations and optimization trade-offs. The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. 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The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. Later ownership, Python suites, differentiable engines and licensing changes are not attributed retroactively to the original three-author contribution.", "domain": "Robotics simulation and numerical control tools" }, "sources": [ { "citation": "MuJoCo: A physics engine for model-based control", "url": "https://roboti.us/lab/papers/TodorovIROS12.pdf" }, { "citation": "Author publication bibliography: MuJoCo2012 entry", "url": "https://roboti.us/lab/papers.html" } ], "statement": "# MuJoCo: a physics engine designed for control optimization\n\n## A controller needs somewhere to practice\n\nBefore a real robot takes an action, a researcher may want to compare many candidate controllers. A physics engine predicts how a simulated system changes when forces and controls act on it. MuJoCo was designed with this repeated optimization work in mind. Its name refers to multijoint dynamics with contact: connected bodies move, collide and press against one another. The contribution is a research tool for those calculations, not one particular walking policy.\n\n## State and action play different roles\n\nThe state describes quantities such as joint positions and velocities. A control specifies how the system is driven. Forward dynamics predicts motion from the state and control; inverse-dynamics calculations ask which forces or controls correspond to a desired motion under a particular model. Contact makes both tasks harder because bodies may touch or separate. Different mathematical contact formulations trade computation against approximation. An efficiently computed model can still differ from the physical world.\n\n## Estimate a search without inventing a benchmark\n\nConsider a classroom planning budget, not a measurement from the paper. You have two thousand candidate controllers, each evaluated for five hundred simulated steps. That requires one million engine steps. At an assumed fifty thousand steps per second, the engine work alone would take twenty seconds. If the rate halves, it takes forty seconds. This estimate leaves out controller optimization, communication and setup. Always keep those missing costs beside the rate rather than calling the estimate total training time.\n\n## Speed and realism need separate evidence\n\nThe original paper reports results for specified models, contact counts and multicore hardware. It also describes approximations and explicitly leaves further contact-accuracy validation for future work. A controller may exploit a simulator defect instead of learning a physically useful behavior. Faster calculations therefore help research only when the modeled problem remains appropriate. Later MuJoCo ownership, software interfaces and new engine implementations are separate developments, with their own authors and evidence.\n\n## A small project that checks assumptions\n\nAsk your agent to create a budget table varying the number of candidates, steps per candidate and assumed engine rate. Check units and intermediate multiplication before using the totals. Then list the contact assumptions and validation limits stated in the original paper. The output is a bounded planning aid, not a reproduced engine benchmark or a certificate of physical accuracy. It can help another participant decide which quantities must be measured before an expensive experiment begins.\n\n## Scientific scope\n\nContact formulations involve different approximations and optimization trade-offs. The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. Later ownership, Python suites, differentiable engines and licensing changes are not attributed retroactively to the original three-author contribution.\n\n## Sources for this explanation\n\n- [MuJoCo: A physics engine for model-based control](https://roboti.us/lab/papers/TodorovIROS12.pdf): Original 2012 engine paper: design motivation, generalized-coordinate and contact methods, parallel computation, benchmarks and explicit accuracy-validation limits.\n", "summary": "Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit.", "title": "MuJoCo: a physics engine designed for control optimization" }, "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "source_ref": { "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "content_hash": "sha256:f5fbefe0c5beb115d5200f0266844381ba15b66f61cfe182d75f79c378660e33" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:70b07e7ada017381de0e8008d73c23964d8cb700e3892dcb68af4b8f76453021" }, "target": { "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "content_hash": "sha256:f5fbefe0c5beb115d5200f0266844381ba15b66f61cfe182d75f79c378660e33" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "todorov-erez-tassa-mujoco-control-physics-engine-2012", "entry_id": "todorov-erez-tassa-mujoco-control-physics-engine-2012", "revision": 1, "title": "MuJoCo: a physics engine designed for control optimization", "context": "Robotics simulation and numerical control tools", "track": "Reusable scientific method, experimental result or historical framework", "band": "S", "modifier": "-", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-23", "evidence_cutoff": "2026-10-23", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit.", "scope": "Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit. Contact formulations involve different approximations and optimization trade-offs. The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. Later ownership, Python suites, differentiable engines and licensing changes are not attributed retroactively to the original three-author contribution.", "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Contact formulations involve different approximations and optimization trade-offs. The original authors explicitly leave further contact-accuracy validation for future work. Reported throughput concerns specified models, contacts and hardware, with mixed results against some smooth-dynamics baselines; it is not a universal speed or physical-accuracy guarantee. Later ownership, Python suites, differentiable engines and licensing changes are not attributed retroactively to the original three-author contribution.", "references": [ { "title": "MuJoCo: A physics engine for model-based control", "url": "https://roboti.us/lab/papers/TodorovIROS12.pdf", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." }, { "title": "Author publication bibliography: MuJoCo2012 entry", "url": "https://roboti.us/lab/papers.html", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." } ], "roles": [ { "who": "The named authors in the research record", "credit": "SCIENCE", "did": "Source-listed human researchers and engineers for the exact method or resource. The evaluated learning system is not an independently attested scientific author. Earlier methods, funding and data-collection roles remain separate. Individual effort shares and unresolved person identities are not inferred." } ], "target": { "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "content_hash": "sha256:f5fbefe0c5beb115d5200f0266844381ba15b66f61cfe182d75f79c378660e33" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "350000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "todorov-erez-tassa-mujoco-control-physics-engine-2012", "target": { "record_id": "urn:uuid:ede23fb5-7399-4f83-a1b7-ded4e7e1eab4", "version": 1, "content_hash": "sha256:f5fbefe0c5beb115d5200f0266844381ba15b66f61cfe182d75f79c378660e33" }, "sections": [ { "title": "A controller needs somewhere to practice", "text": "Before a real robot takes an action, a researcher may want to compare many candidate controllers. A physics engine predicts how a simulated system changes when forces and controls act on it. MuJoCo was designed with this repeated optimization work in mind. Its name refers to multijoint dynamics with contact: connected bodies move, collide and press against one another. The contribution is a research tool for those calculations, not one particular walking policy." }, { "title": "State and action play different roles", "text": "The state describes quantities such as joint positions and velocities. A control specifies how the system is driven. Forward dynamics predicts motion from the state and control; inverse-dynamics calculations ask which forces or controls correspond to a desired motion under a particular model. Contact makes both tasks harder because bodies may touch or separate. Different mathematical contact formulations trade computation against approximation. An efficiently computed model can still differ from the physical world." }, { "title": "Estimate a search without inventing a benchmark", "text": "Consider a classroom planning budget, not a measurement from the paper. You have two thousand candidate controllers, each evaluated for five hundred simulated steps. That requires one million engine steps. At an assumed fifty thousand steps per second, the engine work alone would take twenty seconds. If the rate halves, it takes forty seconds. This estimate leaves out controller optimization, communication and setup. Always keep those missing costs beside the rate rather than calling the estimate total training time." }, { "title": "Speed and realism need separate evidence", "text": "The original paper reports results for specified models, contact counts and multicore hardware. It also describes approximations and explicitly leaves further contact-accuracy validation for future work. A controller may exploit a simulator defect instead of learning a physically useful behavior. Faster calculations therefore help research only when the modeled problem remains appropriate. Later MuJoCo ownership, software interfaces and new engine implementations are separate developments, with their own authors and evidence." }, { "title": "A small project that checks assumptions", "text": "Ask your agent to create a budget table varying the number of candidates, steps per candidate and assumed engine rate. Check units and intermediate multiplication before using the totals. Then list the contact assumptions and validation limits stated in the original paper. The output is a bounded planning aid, not a reproduced engine benchmark or a certificate of physical accuracy. It can help another participant decide which quantities must be measured before an expensive experiment begins." } ], "references": [ { "title": "MuJoCo: A physics engine for model-based control", "url": "https://roboti.us/lab/papers/TodorovIROS12.pdf", "locator": "Original 2012 engine paper: design motivation, generalized-coordinate and contact methods, parallel computation, benchmarks and explicit accuracy-validation limits." } ] }, "reading_status": "EXPLANATORY_GUIDE" }