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Motion Control of High-Dimensional Musculoskeletal Systems with Hierarchical Model-Based Planning
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Proposes MPC² (MPC with morphology-aware proportional control), a hierarchical sampling-based MPC that plans target joint postures and maps them to 700 muscle activations via Jacobian-scaled proportional control, enabling training-free musculoskeletal locomotion and Bayesian-optimized cost design.
Problem
Real-time, zero-shot motion control of high-dimensional over-actuated musculoskeletal systems (700 muscle-tendon units), where DRL is computationally expensive and MPC typically fails in high-dimensional action spaces.
Approach
A two-level controller: a sampling-based MPPI-style planner optimizes a 37-dimensional joint posture target (with added instant rollouts sampled from the current posture), and a morphology-aware proportional controller converts the target posture into per-actuator controls with gains set from the Jacobian of the current state and target posture.
Key results
- MPC² achieves stable standing and walking control within about 2 minutes, while DynSyn requires at least one day of training for effective control.
- On the Walk task, MPC² reaches a walk distance of 9.50±0.19 m versus 2.05±0.40 m for MPPI and 0 m for gradient descent and iLQG.
- Bayesian optimization of cost weights raises human walking speed from 0.79 m/s to 1.24 m/s and ostrich walking speed from 0.90 m/s to 2.08 m/s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MPC² instead of the strongest listed baseline, MPPI | MS-Human-700 · Human full-body Walk | walk distance: $2.05\pm0.40$ -> $9.50\pm0.19$ | Helped |
| Optimize cost-function weights with Bayesian optimization | MPC² on the human model · Human full-body Walk | walking speed: 0.79 m/s -> 1.24m/s | Helped |
| Optimize cost-function weights with Bayesian optimization | MPC² on the ostrich model · Ostrich Walk | walking speed: 0.90 m/s -> 2.08m/s | Helped |
| Add instant rollouts to posture planning (ablation) | MPC² · Lean-backward Stand | control performance | Helped |
| Use morphology-aware gains instead of constant gains for all actuators (ablation) | MPC² low-level actuator controller · Human full-body Walk | control performance | Helped |
| Use morphology-aware gains instead of PD control (ablation) | MPC² low-level actuator controller · Human full-body Walk | control performance | Helped |
Surprising findings
- MPC reduces muscle activation by over 75% compared to DynSyn during walking despite no energy term in the cost.
- All six MPC baselines from MuJoCo MPC (gradient-based and sampling-based) failed to achieve walking on the full-body model.
Limitations
- Relies on exact simulator dynamics (planning model equals true model), so sim-to-real transfer is not addressed.
- Real-time responsiveness is limited by planning compute; near real-time rather than real-time control, with simulation slowed to 20% (or 1%) speed.
- Per-task cost functions are hand-designed and some tasks use task-specific terms (e.g., stair term).
Experimental setup
Benchmarks: Stand Walk Rough Slope Stair Soccer kick imitation Ostrich walk Arm dexterous manipulation
Metrics: walking distance walking speed time to generate control (clock time) muscle activation sum (energy) success/stability
Baselines: DynSyn MPPI MPO DEP-RL Gradient Descent iLQG Cross Entropy Robust Sampling Sample Gradient
Builds on: MPPI MuJoCo MPC DynSyn
Closest papers by meaning
- Joint-Space Empowerment as a Theory of Dexterous Motor Coordination (ICML 2026 · similarity 0.87)
- World Models as Reference Trajectories for Rapid Motor Adaptation (NeurIPS 2025 · similarity 0.85)
- Hierarchical World Models as Visual Whole-Body Humanoid Controllers (ICLR 2025 · similarity 0.85)
- Bootstrapped Model Predictive Control (ICLR 2025 · similarity 0.85)
- TD-MPC2: Scalable, Robust World Models for Continuous Control (ICLR 2024 · similarity 0.83)
- Hierarchical Equivariant Policy via Frame Transfer (ICML 2025 · similarity 0.83)
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