将B样条与运动基元结合，提升机器人学习中轨迹的表达能力。
BMP: Bridging the Gap between B-Spline and Movement Primitives
- 用基函数和权重参数重定义B样条，使其具备运动基元特性。
- 在模仿学习与强化学习任务中表现优于现有基元方法。
- 兼顾轨迹平滑性、边界条件满足与高阶统计建模能力。
本文提出B样条运动基元（BMP），一种新型运动基元（MP）变体，利用B样条进行运动表征。B样条因能以少量控制点生成复杂平滑轨迹并满足起止位置与速度约束而广泛用于运动规划，但现有方法忽视轨迹分布的高阶统计特性，限制其在模仿学习（IL）与强化学习（RL）中的应用。相比之下，运动基元擅长捕捉轨迹概率与相关性，但难以直接满足边界条件，常需额外损失项处理速度约束。通过将B样条重构为基于基函数与权重参数的运动基元形式，BMP兼具两者的优点：既保留了精确满足边界条件的能力，又可建模轨迹分布的高阶统计特征。在模仿学习与强化学习任务上的实验证明，BMP显著拓展了B样条在机器人学习中的适用范围，并展现出比现有基元方法更强的表达能力。
原文摘要 · Abstract (English)
This work introduces B-spline Movement Primitives (BMPs), a new Movement Primitive (MP) variant that leverages B-splines for motion representation. B-splines are a well-known concept in motion planning due to their ability to generate complex, smooth trajectories with only a few control points while satisfying boundary conditions, i.e., passing through a specified desired position with desired velocity. However, current usages of B-splines tend to ignore the higher-order statistics in trajectory distributions, which limits their usage in imitation learning (IL) and reinforcement learning (RL), where modeling trajectory distribution is essential. In contrast, MPs are commonly used in IL and RL for their capacity to capture trajectory likelihoods and correlations. However, MPs are constrained by their abilities to satisfy boundary conditions and usually need extra terms in learning objectives to satisfy velocity constraints. By reformulating B-splines as MPs, represented through basis functions and weight parameters, BMPs combine the strengths of both approaches, allowing B-splines to capture higher-order statistics while retaining their ability to satisfy boundary conditions. Empirical results in IL and RL demonstrate that BMPs broaden the applicability of B-splines in robot learning and offer greater expressiveness compared to existing MP variants.
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