Identifying motor synergies -- coordinated hand joint patterns activated at task-dependent time shifts -- from kinematic data is central to motor control and robotics. Existing two-stage methods first extract candidate waveforms (via SVD) and then select shifted templates using sparse optimization, requiring at least two datasets and complicating data collection. We introduce an optimization-based framework that jointly learns a small set of synergies and their sparse activation coefficients. The formulation enforces group sparsity for synergy selection and element-wise sparsity for activation timing. We develop an alternating minimization method in which coefficient updates decouple across tasks and synergy updates reduce to regularized least-squares problems. Our approach requires only a single data set, and simulations show accurate velocity reconstruction with compact, interpretable synergies.
翻译：识别运动协同——即任务依赖时间偏移下激活的协调手部关节模式——是运动控制与机器人学的核心问题。现有两阶段方法首先（通过奇异值分解）提取候选波形，然后使用稀疏优化选择偏移模板，这至少需要两个数据集且使数据收集复杂化。我们提出一种基于优化的框架，可联合学习少量协同及其稀疏激活系数。该公式通过组稀疏性实现协同选择，通过逐元素稀疏性实现激活时序控制。我们开发了一种交替最小化方法，其中系数更新在任务间解耦，协同更新则简化为正则化最小二乘问题。本方法仅需单个数据集，仿真结果表明其能以紧凑且可解释的协同实现精确的速度重建。
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