CDPMM-DMP: Conditional Dirichlet Process Mixture Model-Based Dynamic Movement Primitives

Movement Primitives(MPs) are compact generators for representation and generalization of modular movements, which are usually used to implement learning from demonstration tasks in robotics. Existing works on MPs mostly utilize combinations of basis functions to represent diverse movements, whether employing probabilistic or dynamic approaches. However, applying these approaches requires manual specification of hyperparameters related to basis functions, resulting in inconvenience and a reliance on specific expertise. In this paper, we develop a Conditional Dirichlet Process Mixture Model-based Dynamic Movement Primitive (CDPMM-DMP) to achieve a nonparametric improvement for the Dynamic Movement Primitive (DMP). First, inspired by Bayesian nonparametric theory, we explore the use of the Dirichlet Process Mixture Model (DPMM) to replace the original radial basis functions in the DMP, and construct the required training set from demonstrations. Then, we study the output generation mechanism driven by the DPMM, particularly by employing conditional sampling to avoid the anomalous outputs caused by direct sampling from the DPMM. Finally, we provide analyses of the various properties brought by our nonparametric transformation of DMP. The analyses and validation results show that the proposed CDPMM-DMP can significantly reduce the parameter tuning burden in usage with its nonparametric learning property. Besides, our method still retains the inherent properties of DMP, while also incorporating some properties of probabilistic MPs, such as multi-sample learning and co-activation. Note to Practitioners—This paper is motivated by alleviating the parameter tuning burden of the Dynamic Movement Primitive (DMP) in its learning process. In our research, we address this issue by introducing a nonparametric probabilistic model (namely, Dirichlet process mixture model) into the learning process of DMP to substitute its original deterministic basis functions. This substitution effectively enables our method to automatically identify the required parameters from the demonstration data. To address the subsequent influences of the probabilistic components on the generation process of DMP and its inherent properties, on one hand, we focus on conditional sampling to establish a mechanism for the generation process. This mechanism can prevent the discontinuity and non-convergence of outputs caused by probabilistic sampling. On the other hand, we explore our method to achieve some probabilistic properties of generalization, which the DMP lacks. Simulation and experimental results show our method can achieve nonparametric learning from demonstrations. Additionally, it not only produces smooth and continuous movement from any initial to final states (similar to DMPs), but also holds probabilistic properties such as multi-sample learning and co-activation (similar to probabilistic primitive methods). In practical applications, due to the CDPMM-DMP’s ability of nonparametric learning, it is more user-friendly for general users lacking specialized experience, aligning with the development goals of robot leaning from demonstrations. Moreover, its properties combining deterministic and probabilistic primitive methods make it more potent when facing complex scenarios and various requirements.