Task Space Trajectory Research Articles

A linear model-based simulation tool for estimating number of trials needed for upper limb stroke recovery in a given rehabilitation session

Traditional methods for assessing upper-limb functional outcomes in stroke patients often fail to estimate the number of trials required to achieve performance stability of a chosen kinematic metric. Limited non-model-based studies have attempted to tackle this issue. To bridge this gap, this study utilized an iterative learning algorithm (ILA) in MATLAB, employing linear models to represent the muscle dynamics and forearm extension of impaired patients. The reference task space trajectory was set as a straight-line point-point trajectory within a range of 0 - 0.2828m. By using the root mean square error (RMSE) as a metric for evaluating kinematic accuracy, a maximum kinematic deviation error of 0.01m was imposed with respect to the trajectory by the (ILA). Results indicate that over 16 trials, performance stability was obtained with improvement in deviation error from 0.0168m in the first trial to 0.0060 at sixteen trials. The result obtained is in line with similar non-model studies and our findings inform the potential of ILAs with linear models for estimation of trial numbers required to attain performance stability of a selected kinematic metric (i.e., kinematic accuracy).

A Time-Optimal Continuous Jerk Trajectory Planning Algorithm for Manipulators

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

Probabilistic Dual-Space Fusion for Real-Time Human-Robot Interaction.

For robots in human environments, learning complex and demanding interaction skills from humans and responding quickly to human motions are highly desirable. A common challenge for interaction tasks is that the robot has to satisfy both the task space and the joint space constraints on its motion trajectories in real time. Few studies have addressed the issue of hyperspace constraints in human-robot interaction, whereas researchers have investigated it in robot imitation learning. In this work, we propose a method of dual-space feature fusion to enhance the accuracy of the inferred trajectories in both task space and joint space; then, we introduce a linear mapping operator (LMO) to map the inferred task space trajectory to a joint space trajectory. Finally, we combine the dual-space fusion, LMO, and phase estimation into a unified probabilistic framework. We evaluate our dual-space feature fusion capability and real-time performance in the task of a robot following a human-handheld object and a ball-hitting experiment. Our inference accuracy in both task space and joint space is superior to standard Interaction Primitives (IP) which only use single-space inference (by more than 33%); the inference accuracy of the second order LMO is comparable to the kinematic-based mapping method, and the computation time of our unified inference framework is reduced by 54.87% relative to the comparison method.

Offline Trajectory Generation for Bipedal Robot Using Linear Inverted Pendulum Model

Reduced order model (ROM)-based controllers have proved to be effective to generate stable bipedal locomotion. However, it is important to understand the limitations and effectiveness of these models without implementing any controllers. This study highlights the versatility of the Linear Inverted Pendulum Model (LIPM) at various walking speeds. Firstly, the Centre of Mass (COM) trajectory has been generated using the LIPM model, and the foot motion trajectory has been created using a sixth-order polynomial function. The trajectory is generated using a predefined step length, speed of locomotion and COM height. Secondly, the task space trajectory has been converted into a joint space trajectory through inverse kinematics for a 6-degree-of-freedom leg. To facilitate the proper walking motion the contact between the foot sole and the ground is implemented. Finally, a simple bipedal robot in MATLAB/Simulink has been modelled and the generated trajectories were implemented.

Design development and control of a shape memory alloy linear actuation based XYθ motion stage

This article addresses the development and trajectory tracking analysis of the three degrees of freedom Shape memory alloy (SMA) actuation-based 4- P PR motion stage. The developed motion stage is of four legs of the PPR (Prismatic-Prismatic-Revolute) configuration, having the first prismatic joint as the active joint. SMA spring is incorporated as the linear actuator of the motion stage. The three degrees of freedom motion of the end-effector is achieved based on a new type of SMA-driven PPR joint configuration to provide two translations and one rotational motion. The advantages of the SMA as an actuator is such as lightweight, higher accuracy, and micron-level movement to establish linear motion and silent actuation. The kinematic and jacobian relations are derived for the developed motion stage. The actuation of the SMA (Nitinol) spring actuator is accomplished by the use of a programmable power supply. In addition, the close loop PID control scheme to the SMA linear actuator is investigated. The mechanism has some inherent errors, as geometric errors (kinematic error), friction between the elements of the mechanism, etc, are significant issues in tracking the trajectory of the motion stage. Thus, to address the above issues, this study incorporates the dual-loop control scheme for better trajectory tracking and error compensation of the proposed motion stage. The control method employs a redundant feedback approach, in which discrete joint space displacements and mobile platform coordinates, and task space coordinates are determined as feedback signal using suitable sensors. In this control scheme, the actual joint displacement errors are computed using the redundant feedback data and corrected the desired joint displacement trajectory to obtain the desired task space trajectory. To measure the effectiveness of the used control scheme, a real-time prototype of the proposed motion stage (4- P PR) is developed and investigated the performance of the control method using some simple geometric trajectories. It is observed from the experiments that the motion stage using SMA linear actuation technique has good tracking performance using the control scheme. The developed motion stage can be implemented in the micro-stereolithography process and micron-level positioning application.

Vision-Based Impedance Control of an Aerial Manipulator Using a Nonlinear Observer

Contact-based aerial interaction control in unknown environments is a challenging issue. To solve this problem, this paper presents an image-based impedance control scheme for an aerial manipulator. Unlike points and image moments, the line features considered in this paper cannot uniquely determine the pose of the onboard camera. Therefore, a nonlinear observer is proposed to online provide supplementary 3D information of the system. After that, a hierarchical tracking controller, which is equipped with an image-space impedance filter, is designed to implement a trajectory tracking task with tunable compliance, while at the same time achieving a subtask that aims to determine the final pose of the aerial manipulator. By planning task-space trajectories, desired interaction behavior can be specified without relying on the global position of the system. Furthermore, the effectiveness criterion of the observer is derived, and the stability of the system is proven. Several experiments, including a push-and-slide task, robustness analysis, and a comparison with the state of the art have been conducted to demonstrate the feasibility of the method. Note to Practitioners—This article presents a method for controlling an aerial manipulator to interact with unknown environments without measuring the global position of both the environment and the aerial manipulator. Furthermore, unlike the existing methods, the proposed visual servoing method is based on line features, which are generally more robust than point features. Moreover, it would be intuitive for users to specify the approaching path and the interaction behavior of the aerial manipulator by just planning the image feature trajectories and the desired distance between the aerial manipulator and the environment. This distance is online estimated using the visual feedback of a monocular camera, instead of relying on any costly 3D-vision sensors or lidars, making it an economical solution for aerial manipulation in field environments.

Gaussian-process-based robot learning from demonstration

AbstractLearning from demonstration allows to encode task constraints from observing the motion executed by a human teacher. We present a Gaussian-process-based learning from demonstration (LfD) approach that allows robots to learn manipulation skills from demonstrations of a human teacher. By exploiting the potential that Gaussian process (GP) models offer, we unify in a single, entirely GP-based framework, the main features required for a state-of-the-art LfD approach. We address how GP can be used to effectively learn a policy from trajectories in task space. To achieve an effective generalization across demonstrations, we propose the novel Task Completion Index (TCI) for temporal alignment of task trajectories. Also, our probabilistic GP-based representation allows encoding variability throughout the different phases of the task. Finally, we present a method to efficiently adapt the policy to fulfill new requirements and modulate the robot behavior as a function of task variability. This approach has been successfully tested in a real-world application, namely teaching a TIAGo robot to open different types of doors.

Neural-Dynamics Optimization and Repetitive Learning Control for Robotic Leg Prostheses

Rapid development in robotics and bionics makes it possible for robotic leg prostheses to help amputees while imposing challenges on duplicating the motion characteristics of the amputees’ healthy leg. One critical problem in prosthetic control is joint angle drift problem, that is, a repetitive motion trajectory in task space cannot guarantee that the generated motion trajectories in joint space are also repetitive. In order to solve this problem, in this article, we propose neural-dynamics optimization for robotic leg prostheses to generate the repetitive joint trajectories in real time. Our proposed method duplicates the self-selected walking speed of the amputees’ healthy leg. The online motion generation is formulated as a constrained quadratic programming (QP) optimization problem whose objective function adopts the kinetic energy and joint displacement performance criterion. The varying parameter convergent differential neural network is developed as a real-time QP solver which can globally converge to the optimal solution of the constrained QP problem. Then, a repetitive learning controller is designed for robotic leg prostheses to reduce the tracking errors while following the repetitive motion. Through the physical experiments on the developed two-degree-of-freedom robotic leg prosthesis worn on an amputee, the neural-dynamics optimization is substantiated to be a remedy of online motion generation, and the effectiveness of repetitive learning control for reducing the prosthetic tacking errors is verified.

A General Approach for the Automation of Hydraulic Excavator Arms Using Reinforcement Learning

This article presents a general approach to derive an end effector trajectory tracking controller for highly nonlinear hydraulic excavator arms. Rather than requiring an analytical model of the system, we use a neural network model that is trained based on measurements collected during operation of the machine. The data-driven model effectively represents the actuator dynamics including the cylinder-to-joint-space conversion. Requiring only the distances between the individual joints, a simulation is set up to train a control policy using reinforcement learning (RL). The policy outputs pilot stage control commands that can be directly applied to the machine without further fine-tuning. The proposed approach is implemented on a Menzi Muck M545, a 12 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{t}$</tex-math></inline-formula> hydraulic excavator, and tested in different task space trajectory tracking scenarios, with and without soil interaction. Compared to a commercial grading controller, which requires laborious hand-tuning by expert engineers, the learned controller shows higher tracking accuracy, indicating that the achieved performance is sufficient for the practical application on construction sites and that the proposed approach opens a new avenue for future machine automation.

Reinforcement Learning-Based Cascade Motion Policy Design for Robust 3D Bipedal Locomotion

This paper presents a novel reinforcement learning (RL) framework to design cascade feedback control policies for 3D bipedal locomotion. Existing RL algorithms are often trained in an end-to-end manner or rely on prior knowledge of some reference joint or task space trajectories. Unlike these studies, we propose a policy structure that decouples the bipedal locomotion problem into two modules that incorporate the physical insights from the nature of the walking dynamics and the well-established Hybrid Zero Dynamics approach for 3D bipedal walking. As a result, the overall RL framework has several key advantages, including lightweight network structure, sample efficiency, and less dependence on prior knowledge. The proposed solution learns stable and robust walking gaits from scratch and allows the controller to realize omnidirectional walking with accurate tracking of the desired velocity and heading angle. The learned policies also perform robustly against various adversarial forces applied to the torso and walking blindly on a series of challenging and unstructured terrains. These results demonstrate that the proposed cascade feedback control policy is suitable for navigation of 3D bipedal robots in indoor and outdoor environments.

An Efficient Stochastic Constrained Path Planner for Redundant Manipulators

This brief proposes a novel stochastic method that exploits the particular kinematics of mechanisms with redundant actuation and a well-known manipulability measure to track the desired end-effector task-space motion in an efficient manner. Whilst closed-form optimal solutions to maximise manipulability along a desired trajectory have been proposed in the literature, the solvers become unfeasible in the presence of obstacles. A manageable alternative to functional motion planning is thus proposed that exploits the inherent characteristics of null-space configurations to construct a generic solution able to improve manipulability along a task-space trajectory in the presence of obstacles. The proposed Stochastic Constrained Optimization (SCO) solution remains close to optimal whilst exhibiting computational tractability, being an attractive proposition for implementation on real robots, as shown with results in challenging simulation scenarios, as well as with a real 7R Sawyer manipulator, during surface conditioning tasks.

Learning Kinematic Feasibility for Mobile Manipulation Through Deep Reinforcement Learning

Mobile manipulation tasks remain one of the critical challenges for the widespread adoption of autonomous robots in both service and industrial scenarios. While planning approaches are good at generating feasible whole-body robot trajectories, they struggle with dynamic environments as well as the incorporation of constraints given by the task and the environment. On the other hand, dynamic motion models in the action space struggle with generating kinematically feasible trajectories for mobile manipulation actions. We propose a deep reinforcement learning approach to learn feasible dynamic motions for a mobile base while the end-effector follows a trajectory in task space generated by an arbitrary system to fulfill the task at hand. This modular formulation has several benefits: it enables us to readily transform a broad range of end-effector motions into mobile applications, it allows us to use the kinematic feasibility of the end-effector trajectory as a dense reward signal and its modular formulation allows it to generalise to unseen end-effector motions at test time. We demonstrate the capabilities of our approach on multiple mobile robot platforms with different kinematic abilities and different types of wheeled platforms in extensive simulated as well as real-world experiments.

Task-Space Trajectory Tracking Control for Coordinated Manipulation Using Sampled Coupling Data

This letter studies the task-space synchronization control problem of networked manipulators which are commanded to track the desired task-space trajectories to achieve the coordinated manipulation transportation tasks in industrial and logistic applications. To guarantee the practical applicability and increase information transmission efficiency, sampled data-coupling strategy is utilized and the transmission delays as well as dynamics uncertainties are modelled explicitly. Firstly, the discrete-time-style synchronization error with sampled data is transferred into an equivalent continuous-time version with time-varying communication delays. Secondly, a distributed task-space tracking control law is presented based on the dynamic model by introducing the task-space end-position synchronization error for coordinated manipulation tasks of networked manipulators. Thirdly, a sufficient condition is derived from the Lyapunov-Krasovskii stability analysis approach to ensure the convergence of the dynamic control of each manipulator. By solving the proposed condition, the upper bound of the acceptable sampling period can be calculated. Simulational experiment results on a group of PUMA560 manipulators validate the task-space trajectory tracking performance, end-position synchronization performance and robustness to external force interference of the multiple-manipulator systems. To the best knowledge of the authors, this is the first letter which resolves the task-space tracking control of coordinated manipulators in the presence of coupling data sampling, transmission delays and dynamics model uncertainties.

Fractional-order resolved acceleration control for free-floating space manipulator with system uncertainty

This paper investigates the task-space trajectory tracking control of free-floating space manipulator (FFSM) with system uncertainty considered. The dynamics of the FFSM, as well as the mapping between the task space and the joint space, are first established. To estimate and compensate for the uncertainty, a disturbance observer is designed which ensures the estimation error converges to zero within finite time. To improve the task-space tracking performance, the fractional-order resolved acceleration control (FORAC) scheme is proposed. The proposed control method utilizes the fractional-order integral to construct a sliding surface and stirs the tracking error to converge along this surface, which improves the robustness and transient performance of the entire system. Besides, the estimated uncertainty is introduced into the controller to compensate for the influence of actual system uncertainty, and reduce the control gains. Theoretical analysis is given to show the closed-loop behavior of the proposed controller and observer. Simulations are conducted to verify the effectiveness of the proposed method.

Task Space Trajectory Planning for Robot Manipulators to Follow 3-D Curved Contours

The demand for robots has increased in the industrial field, where robots are utilized in tasks that require them to move through complex paths. In the motion planning of a manipulator, path planning is carried out to determine a series of the positions of robot end effectors without collision. Therefore, it is necessary to carry out trajectory planning to determine position, velocity, and acceleration over time and to control an actual industrial manipulator. Although several methods have already been introduced for point-to-point trajectory planning, a trajectory plan which moves through multiple knots is required to allow robots to adapt to more complicated tasks. In this study, a trajectory planning based on the Catmull–Rom spline is proposed to allow a robot to move via several points in a task space. A method is presented to assign intermediate velocities and time to satisfy the velocity conditions of initial and final knots. To optimize the motion of the robot, a time-scaling method is presented to minimize the margin between the physical maximum values of velocity and acceleration in real robots and the planned trajectory, respectively. A simulation is then performed to verify that the proposed method can plan the trajectory for moving multiple knots without stopping, and also to check the effects of control parameters. The results obtained show that the proposed methods are applicable to trajectory planning and require less computation compared with the cubic spline method. Furthermore, the robot follows the planned trajectory, and its motion does not exceed the maximum values of velocity and acceleration. An experiment is also executed to prove that the proposed method can be applied to real robotic tasks to dispense glue onto the sole in the shoe manufacturing process. The results from this experiment show that the robot can follow the 3-D curved contour in uniform speed using the proposed method.

Hierarchical Impedance-Based Tracking Control of Kinematically Redundant Robots

The control of a robot in its task space is a standard approach nowadays. If the system is kinematically redundant with respect to this goal, one can even execute additional subtasks simultaneously. By utilizing null space projections, for example, the whole stack of tasks can be implemented within a strict task hierarchy following the order of priority. One of the most common methods to track multiple task-space trajectories at the same time is to feedback-linearize the system and dynamically decouple all involved subtasks, which finally yields the exponential stability of the desired equilibrium. In this article, we provide a hierarchical multi-objective controller for trajectory tracking that ensures both asymptotic stability of the equilibrium and a desired contact impedance at the same time. In contrast to the state of the art in prioritized multi-objective control, feedback of the external forces can be avoided and the natural inertia of the robot is preserved. The controller is evaluated in simulations and on a standard lightweight robot with torque interface. The approach is predestined for precise trajectory tracking where dedicated and robust physical-interaction compliance is crucial at the same time.

Exponential Tracking Control of Robotic Manipulators With Uncertain Dynamics and Kinematics

This paper addresses a long-standing yet well documented open problem on task-space trajectory tracking control of robotic manipulators subject to both uncertain dynamics and uncertain kinematics. The main contribution is to establish a theoretical framework for designing an observer-based controller to achieve exponential tracking control. Two observers are designed for precisely estimating the uncertain kinematics and dynamics. It is theoretically proved that the entire observer–controller system is proved to be globally exponentially stable. Both the estimation errors and the trajectory tracking error can globally exponentially converge to their stable equilibrium points, respectively. To the best knowledge of the author, this works may be the first result for robot exponential tracking control. The tracking performance is, therefore, more robust to system uncertainties. The settling time of the closed-loop tracking error system can be tuned to be small arbitrarily. Experimental tests are also conducted to validate the effectiveness of the designed control framework.

High-precision trajectory tracking design and simulation for six degree of freedom robot based on improved active disturbance rejection control

High-precision trajectory tracking control is an important factor in the performance of industrial robots. In this study, a high-precision trajectory tracking strategy was proposed for controlling a degree of freedom serial robot on the basis of improved active disturbance rejection control. An independent control strategy of a single joint was adopted, and the corresponding decoupling control law was designed. An attitude trajectory-planning algorithm based on the circular-blending quaternion curve was improved. The position and attitude trajectories were transformed into the joint trajectory by using a kinematics equation and inverse velocity Jacobian matrix. The above-mentioned transformation link was used as a preprocessing link of the active disturbance rejection control, which is used for replacing the tracking differentiator of a typical active disturbance rejection control to eliminate the effect of the tracking delay. An experimental simulation was conducted by combining MATLAB and ADAMS. Simulation results show that the proposed control strategy can perform the tracking control of a task-space trajectory. The tracking precision of position and attitude trajectories were 0.01 mm and 0.01 s, respectively.

Kinematic optimization for bipedal robots: a framework for real-time collision avoidance

Bipedal locomotion is more than dynamically stable walking. The redundant kinematic design of humanoid robots allows for complex motions in complex scenarios. One challenge of current robotic research is the exploitation of the capacities of redundant robots in real-time applications. In this paper, we present and evaluate methods for real-time motion generation of redundant robots. The proposed methods are based on a model-predictive approach. We propose and compare methods for optimization of robot motions defined by parameterized task-space trajectories and for redundancy resolution. The approaches are successfully combined in a novel algorithm. The methods are introduced with the help of a minimal model. It shows their applicability for a wide range of complex robotic systems. We apply and validate their effectiveness and their real-time character in several experiments with different environments with the humanoid robot Lola.

Kinematically Optimal Robust Control of Redundant Manipulators

This work deals with the problem of the robust optimal task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the endeffector. Furthermore, the movement is to be accomplished in such a way as to minimize both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of chattering-free robust kinematically optimal controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.