Visualization of Stable Heteroclinic Channel-Based Movement Primitives

Dynamic systems which underlie controlled systems are expected to increase in complexity as robots, devices, and connected networks become more intelligent. While classical stable systems converge to a stable point (a sink), another type of stability is to consider a stable path rather than a single point. Such stable paths can be made of saddle points that draw in trajectories from certain regions, and then push the trajectory toward the next saddle point. These chains of saddles are called stable heteroclinic channels (SHCs) and can be used in robotic control to represent time sequences. While we have previously shown that each saddle is visualizable as a trajectory waypoint in phase space, how to increase the fidelity of the trajectory was unclear. In this paper, we hypothesized that the waypoints can be individually modified to locally vary fidelity. Specifically, we expected that increasing the saddle value (ratio of saddle eigenvalues) causes the trajectory to slow to more closely approach a particular saddle. Combined with other parameters that control speed and magnitude, a system expressed with an SHC can be modified locally, point by point, without disrupting the rest of the path, supporting their use in motion primitives. While some combinations can enable a trajectory to better reach into corners, other combinations can rotate, distort, and round the trajectory surrounding the modified saddle. Of the system parameters, the saddle value provides the most predictable tunability across 3 orders of magnitude.

Dynamic movement primitives (DMPs) are a learning from demonstration (LfD) method that imitates movement primitives. Recently, reinforcement learning (RL) has been used to modify DMPs. In this regard, most methods have concentrated on improving DMPs with RL after DMPs are learned with supervised learning. In this way, there is no guarantee that the DMPs stay close to demonstrations while modified. To address this problem, in this study, a framework is proposed for learning DMPs with deep RL, which can be further used to modify DMPs. To do so, first, DMPs are modeled in the framework of deep RL. Then, after the reward function for learning is defined, they are learned with deep RL. The deep RL algorithm used in the present study is the twin-delayed deep deterministic policy gradient (TD3) algorithm. Our proposed algorithm is evaluated with various demonstrations, and a case study of a pick-and-place task is done. The results show that our method can learn all demonstrations with high accuracy.

Dynamic movement primitives are one of key concepts for understanding dexterous and flexible movements of biological bodies. In the field of robotics engineering, simple types of nonlinear differential equations are used to generate movement primitives from demonstrations, but it remains unclear how nonlinear dynamics in the real brain can also generate movement primitives in biologically natural ways. The aim of this study is to investigate a possible role of nonlinear dynamics in random recurrent neural networks (RNNs) for skillful motor learning. We show that one-shot temporal patterns such arm reaching movements can be trained by a type of RNN-learning so-called FORCE-learning recently proposed by Sussillo and Abbott and a number of patterns are summarized as a manifold embedded in a space of synaptic weights of readout neurons. We also discuss how generalization of learning against untrained motor patterns can be achieved by identifying nonlinear coordinates (meta-parameters) on this manifold in a higher level of the central nervous system.

Segmenting complex movements into a sequence of primitives remains a difficult problem with many applications in the robotics and vision communities. In this work, we show how the movement segmentation problem can be reduced to a sequential movement recognition problem. To this end, we reformulate the original Dynamic Movement Primitive (DMP) formulation as a linear dynamical system with control inputs. Based on this new formulation, we develop an Expectation-Maximization algorithm to estimate the duration and goal position of a partially observed trajectory. With the help of this algorithm and the assumption that a library of movement primitives is present, we present a movement segmentation framework. We illustrate the usefulness of the new DMP formulation on the two applications of online movement recognition and movement segmentation.

The paper addresses the problem of learning internal task-specific dynamic models for a reaching task. Using task-specific dynamic models is crucial for achieving both high tracking accuracy and compliant behaviour, which improves safety concerns while working in unstructured environment or with humans. The proposed approach uses programming by demonstration to learn new task-related movements encoded as Compliant Movement Primitives (CMPs). CMPs are a combination of position trajectories encoded in a form of Dynamic Movement Primitives (DMPs) and corresponding task-specific Torque Primitives (TPs) encoded as a linear combination of kernel functions. Unlike the DMPs, TPs cannot be directly acquired from user demonstrations. Inspired by the human sensorimotor learning ability we propose a novel method which autonomously learns task-specific TPs, based on a given kinematic trajectory in DMPs.

Purpose This paper aims to solve the problem of the inability to apply learning methods for robot motion skills based on dynamic movement primitives (DMPs) in tasks with explicit environmental constraints, while ensuring the reliability of the robot system. Design/methodology/approach The authors propose a novel DMP that takes into account environmental constraints to enhance the generality of the robot motion skill learning method. First, based on the real-time state of the robot and environmental constraints, the task space is divided into different regions and different control strategies are used in each region. Second, to ensure the effectiveness of the generalized skills (trajectories), the control barrier function is extended to DMP to enforce constraint conditions. Finally, a skill modeling and learning algorithm flow is proposed that takes into account environmental constraints within DMPs. Findings By designing numerical simulation and prototype demonstration experiments to study skill learning and generalization under constrained environments. The experimental results demonstrate that the proposed method is capable of generating motion skills that satisfy environmental constraints. It ensures that robots remain in a safe position throughout the execution of generation skills, thereby avoiding any adverse impact on the surrounding environment. Originality/value This paper explores further applications of generalized motion skill learning methods on robots, enhancing the efficiency of robot operations in constrained environments, particularly in non-point-constrained environments. The improved methods are applicable to different types of robots.

Kinesthetic teaching and Dynamic Movement Primitives (DMPs) enable fast and adaptable learning of robot tasks based on a human demonstration. A task encoded as a dynamic movement primitive can be reused with a different goal position, albeit with a resulting distortion in the approach trajectory with regards to the original task. While this is sufficient for some robotic applications, the accuracy requirements for assembly tasks in an industrial context, where tolerances are tight and workpieces are small, is much higher. In such a context it is also preferable to keep the number of demonstrations and of external sensors low. Our approach relies on a single demonstration and a single force-torque sensor at the robot tool. We make use of a Convolutional Neural Network (CNN) trained on the force-torque sensor data to segment the task into several movement primitives for the different phases: pickup - approach - insertion - retraction, allowing us to achieve better positional accuracy when generalizing the task primitives to new targets. To the best of our awareness, we are the first to utilize a CNN as a segmentation tool to improve the generalization performance of DMPs.

Movement generation, and especially generalization to unseen situations, plays an important role in robotics. Different types of movement generation methods exist such as spline based methods, dynamical system based methods, and methods based on Gaussian mixture models (GMMs). Using a large, new dataset on human manipulations, in this paper we provide a highly detailed comparison of five fundamentally different and widely used movement encoding and generation frameworks: dynamic movement primitives (DMPs), time based Gaussian mixture regression (tbGMR), stable estimator of dynamical systems (SEDS), Probabilistic Movement Primitives (ProMP) and Optimal Control Primitives (OCP). We compare these frameworks with respect to their movement encoding efficiency, reconstruction accuracy, and movement generalization capabilities. The new dataset consists of nine object manipulation actions performed by 12 humans: pick and place, put on top/take down, put inside/take out, hide/uncover, and push/pull with a total of 7,652 movement examples. Our analysis shows that for movement encoding and reconstruction DMPs and OCPs are the most efficient with respect to the number of parameters and reconstruction accuracy, if a sufficient number of kernels is used. In case of movement generalization to new start- and end-point situations, DMPs, OCPs and task parameterized GMM (TP-GMM, movement generalization framework based on tbGMR) lead to similar performance, which ProMPs only achieve when using many demonstrations for learning. All models outperform SEDS, which additionally proves to be difficult to fit. Furthermore we observe that TP-GMM and SEDS suffer from problems reaching the end-points of generalizations. These different quantitative results will help selecting the most appropriate models and designing trajectory representations in an improved task-dependent way in future robotic applications. • Comparison of five motion encoding frameworks on human manipulation action dataset. • Large dataset containing 7652 movement trajectories from 9 different action classes. • Comparison regarding encoding and generalization reveals model specific differences.

Addressing the limitations of traditional Dynamic Movement Primitives (DMP) obstacle avoidance methods-which rely on dynamic coupling terms leading to complex algorithmic structures, sluggish responses, and difficulties in autonomous obstacle avoidance-this study innovatively proposes a robotic arm obstacle avoidance trajectory planning framework that integrates DMP with the Informed RRT* algorithm. This framework uses the Informed RRT algorithm to do local trajectory replanning in areas near obstacles. It keeps the main dynamic features of DMP and creates obstacle-avoidance trajectories that are then smoothly added to the original DMP trajectory. This approach eliminates the need for complex dynamic coupling terms, significantly reducing algorithmic complexity. Its local replanning mechanism not only enables autonomous obstacle avoidance and effectively suppresses trajectory oscillations but also substantially enhances real-time response speed. The main contributions of this study include 1) proposing a decoupled DMP obstacle avoidance method based on local trajectory replanning combined with Informed RRT*, simplifying the algorithm structure; 2) the adopted local replanning strategy significantly shortens response time and improves obstacle avoidance efficiency. The effectiveness of the proposed algorithm was validated through two sets of comparative experiments (against the RRT method) conducted on a collaborative robot platform. Experimental results demonstrate that the algorithm reduces response time for obstacle avoidance by 33.2% and increases success rate by 19.5%, fully proving its potential and applicability in specific industrial scenarios.

Dynamic Movement Primitives (DMPs) are a well-known tool for encoding robotic motions. Their popularity stems from invariance properties in time and space, the ability to describe complex coordinated motions in multiple degrees of freedom with a relatively small number of parameters, and the linearity in the parameters that describe the motion. The latter allows easily fitting a DMP to motions e.g. demonstrated by a human. DMPs are at their core second order autonomous differential equations. However, feedforward controls of robots with flexible joints are known to require reference trajectories up to the fourth derivative of position. Consequently, classical DMPs are mechanically not compatible with flexible joint robots. In this paper, we propose an extension of DMPs by introducing FlexDMPs. This concept retains the structural properties and benefits of classical DMPs but generates trajectories up to the fourth derivative that can theoretically be tracked ideally (i.e. with zero tracking error) by flexible joint robots. The concept is demonstrated on a high fidelity simulation model of an industrial robot and in experimental results on a collaborative manipulator.

An essential aspect for making robots succeed in real-world environments is to give them the ability to robustly perform motions in continuously changing situations. Classical motion planning methods usually create plans for static environments. The direct execution of such plans in dynamic environments often becomes problematic. We present an approach that adapts motion plans by feeding changes of the environment into a transformation of the plan in task space. Furthermore, the progress in the plan is defined with a phase variable that is updated adaptively according to the actual task progress. This phase variable releases the strict time compliance that many motion planning methods bring along. The main benefit of our approach is the ability to do this adaptation in a computational efficient manner during the execution of the motion. Thus, the gap between the motion planning and motion execution stage is bridged by continuously transforming geometric and dynamic features of a reference plan to the current situation. We evaluate the performance of our approach by comparing it to alternative methods such as dynamic motion primitives and continuous replanning on several simulated benchmark tasks. Moreover, we demonstrate the real robot applicability on a PR2 robot platform.

We explore the potential for humanoid robots to interact with humans in hand-clapping games. In this context, a robot is able to adapt to random hand motions of humans in a timely fashion without preplaned information. This capability is built through: (1) predict human future motions in real time at very early stages (2) prediction involved in the robot dynamic systems for continuous movement control. We use Probability Movement Primitives (ProMPs) for human motion prediction and improved the accuracy through a motion recognition process with Heininger distance. To encode the possibility region of future human motions, a implicit Dynamic Movement Primitives (DMPs) is generated capturing different dynamics on one short for robot motion model. At last Model Predictive Controller (MPC) is applied to track K-step forward human motions to achieve time synchronization and joint goals. We present the results obtained for various hand-to-hand contacts between NAO robot and kids.

Solution of nonlinear partial differential equations from base equations

In order to properly function in real-world environments, the gait of a humanoid robot must be able to adapt to new situations as well as to deal with unexpected perturbations. A promising research direction is the modular generation of movements that results from the combination of a set of basic primitives. Humans seem to be able to adapt their motion in an effortless way and efficient way. In this work we present a methodology to extract a single demonstration signal from a human teacher that can be used in a biped robot to walk in an efficient way and quickly adapt to new situations. Instead of using a normal human gait, the demonstrator walks on a gait we called "robot-like". It is our belief that the retargeting task will be more efficient and easier by using this methodology. The acquired signal is then used to train a set of Dynamic Movement Primitives (DMP) that directly retrieves the trajectories of the end effector in the Cartesian space. In previous works we have used this methodology with efficiency in several tasks, e.g., walking over irregularities, overcoming an obstacle. Now, by combining rhythmic DMP with discrete DMP, we show that the adaptability performance to new situations that require precise foot placement is increased.

Forestry cranes are an important tool for safe and efficient timber harvesting with forestry machines. However, their complex manual control often led to inefficiencies and excessive energy usage, due to the many joysticks and buttons that must be used in a precise sequence to perform efficient movements. To address this, the industry is increasingly turning to partial automation, making manual control more intuitive for the operator and, consequently, achieving improvements in energy efficiency. This article introduces a novel approach to energy-optimal motion planning that can be used along with a feedback control system to automate crane motions, taking over portions of the operator’s work. Our method combines dynamic movement primitives (DMPs) and an energy-optimization algorithm. DMPs is a machine learning technique for motion planning based on human demonstrations, while the optimization algorithm exploits the crane’s redundancy to find energy-optimal trajectories. Simulation results show that DMPs can replicate human-like controlled motions with a 25% reduction in energy consumption. However, our energy optimization algorithm shows improvements of over 40%, providing substantial energy savings and a promising pathway towards environmentally friendly partially automated machines.