Joint Trajectory Generation Research Articles

Design and Position Control of a Robot with 5 Degrees of Freedom

In recent decades, robotics and artificial intelligence have gained significant importance for their involvement in various industrial processes currently at their peak. Nevertheless, advanced robots are not designed explicitly for lemon supply. This research aims to develop a manipulator robot with 5 degrees of freedom and control its trajectories for lemon supply purposes. To achieve this goal, kinematic and dynamic calculations of the manipulator robot were performed, along with the development of programming code in Matlab to determine its trajectories, positions, speeds, and accelerations. In addition, the Proportional Integral Derivative (PID) tuner was used to obtain the optimal controller parameters and ensure accurate joint trajectory generation.

Multi-Objective Swarm Intelligence Trajectory Generation for a 7 Degree of Freedom Robotic Manipulator

This work is aimed to demonstrate a multi-objective joint trajectory generation algorithm for a 7 degree of freedom (DoF) robotic manipulator using swarm intelligence (SI)—product of exponentials (PoE) combination. Given a priori knowledge of the end-effector Cartesian trajectory and obstacles in the workspace, the inverse kinematics problem is tackled by SI-PoE subject to multiple constraints. The algorithm is designed to satisfy finite jerk constraint on end-effector, avoid obstacles, and minimize control effort while tracking the Cartesian trajectory. The SI-PoE algorithm is compared with conventional inverse kinematics algorithms and standard particle swarm optimization (PSO). The joint trajectories produced by SI-PoE are experimentally tested on Sawyer 7 DoF robotic arm, and the resulting torque trajectories are compared.

Quadrupedal Human-Assistive Robotic Platform (Q-HARP): Design, Control, and Preliminary Testing

Abstract With the rapid expansion of older adult populations around the world, mobility impairment is becoming an increasingly challenging issue. For the assistance of individuals with mobility impairments, there are two major types of tools in the current practice, including the passive (unpowered) walking aids (canes, walkers, rollators, etc.) and wheelchairs (powered and unpowered). Despite their extensive use, there are significant weaknesses that affect their effectiveness in daily use, especially when challenging uneven terrains are encountered. To address these issues, the authors developed a novel robotic platform intended for the assistance of mobility-challenged individuals. Unlike the existing assistive robots serving similar purposes, the proposed robot, namely, quadrupedal human-assistive robotic platform (Q-HARP), utilizes legged locomotion to provide an unprecedented potential to adapt to a wide variety of challenging terrains, many of which are common in people’s daily life (e.g., roadside curbs and the few steps leading to a front door). In this paper, the design of the robot is presented, including the overall structure of the robot and the design details of the actuated robotic leg joints. For the motion control of the robot, a joint trajectory generator is formulated, with the purpose of generating a stable walking gait to provide reliable support to its human user in the robot’s future application. The Q-HARP robot and its control system were experimentally tested, and the results demonstrated that the robot was able to provide a smooth gait during walking.

Imitating by Generating: Deep Generative Models for Imitation of Interactive Tasks.

To coordinate actions with an interaction partner requires a constant exchange of sensorimotor signals. Humans acquire these skills in infancy and early childhood mostly by imitation learning and active engagement with a skilled partner. They require the ability to predict and adapt to one's partner during an interaction. In this work we want to explore these ideas in a human-robot interaction setting in which a robot is required to learn interactive tasks from a combination of observational and kinesthetic learning. To this end, we propose a deep learning framework consisting of a number of components for (1) human and robot motion embedding, (2) motion prediction of the human partner, and (3) generation of robot joint trajectories matching the human motion. As long-term motion prediction methods often suffer from the problem of regression to the mean, our technical contribution here is a novel probabilistic latent variable model which does not predict in joint space but in latent space. To test the proposed method, we collect human-human interaction data and human-robot interaction data of four interactive tasks “hand-shake,” “hand-wave,” “parachute fist-bump,” and “rocket fist-bump.” We demonstrate experimentally the importance of predictive and adaptive components as well as low-level abstractions to successfully learn to imitate human behavior in interactive social tasks.

Planning Trajectory of Anthropomorphic Walking Robot (Biped Robot)

Humanoid robots have been a topic of great interest for a long time. Among the various motions of a humanoid robot, the most basic and important motion is bipedal walking. Bipedal walking is probably the most appropriate way for robots to move around in a real environment. However Building trajectories for biped robot walking is a complex task considering all degrees of freedom (DOFs) commonly bound within the mechanical structure. To study the stable motion of any bipedal robot we should study the Kinematics, Dynamics, design a control system and of most important the trajectories. This work deals with planning trajectory of humanoid robots (AK Biped robot), especially for planning trajectory of center of mass (CoM), zero moment point (ZMP)a and planning trajectory of swing foot. diffident method used in planning trajectory like 3D linear inverted pendulum (LIMP), polynomial interpolation. The object of study is the process of automatic control walking of an anthropomorphic walking robot (AK biped robot), for that this paper proposes an approach of joint trajectory generation for the biped robot using the three Three-dimensional linear inverted pendulum for planning trajectory of CoM which keep the ZMP to be inside the support polygon which and guarantee stable dynamic walking of AK biped robot, then trajectory of swing foot derived using the polynomial interpolation function for smooth motion. The aim of this paper is to present a full 3D walking strategy using dynamic model of 3D inverted pendulum for generation references joint trajectories with simulation also design a control system that granites a stable walking of Biped Robot. This is done by first reviewing the literature about different walking strategies. During this literature review the 3D-Linear Inverted Pendulum Model appeared to be the most interesting strategy for further research. The idea of the strategy is simple. It models the human as a linear inverted pendulum with massless rods, which represent the legs, and a point mass at the end of the rods representing the total mass of the body. During walking, there is always at least one foot on the ground which can be seen as stance leg. This stance leg is then modeled as an inverted pendulum. The general closed form solution of the dynamics of the linear inverted pendulum are used to design a trajectory for the center of mass (CoM ) for stance leg. In the trajectory generator, the general solution of the 3D-LIPM is used to prescribe a trajectory. for the CoM of the biped robot AK. The trajectory of the swing leg is designed by a cosine velocity profile interpolation function. The joint trajectories are used as the input for a dynamic model of biped robot in SimMechanics. The proposed control system in simulation are carried out to tune the trajectory such that the dynamic model is able to walk balanced and the robustness of the gait was verified by adding of disturbances. For example, the position of the CoM was increased or decreased and the steps were simulated with different ground levels. These simulations showed that the trajectory is relatively robust. Ref. 10, fig. 4.

Safety-oriented robot payload identification using collision-free path planning and decoupling motions

Abstract The paper presents a procedure for the identification of the inertial parameters of the payload mounted on the end-effector of a robotic manipulator operating in a collaborative setup. The procedure is therefore designed considering as a primary objective the safe execution of the payload estimation process, in terms of avoidance of physical objects and protected zones within the robot workspace, in which the presence of human operators is allowed and expected. The methods applied in the definition of the proposed operational sequence include a collision-free path planner and a joint trajectory generator that allows the safe execution of specific test motions. In particular, each one of such test motions decouples the effects of all but one inertial parameter of the payload, in order to improve the accuracy of identification. Experimental results on a redundant industrial manipulator demonstrate the feasibility of the proposed identification method.

Joint trajectory generator for powered orthosis based on gait modelling using PCA and FFT

SUMMARYIn this work, we propose a method able to find user-oriented gait trajectories that can be used in powered lower limb orthosis applications. Most research related to active orthotic devices focuses on solving hardware issues. However, the problem of generating a set of joint trajectories that are user-oriented still persists. The proposed method uses principal component analysis to extract shared features from a gait dataset, taking into consideration gait-related variables such as joint angle information and the user's anthropometric features, used directly in an orthosis application. The trajectories of joint angles used by the model are represented by a given number of harmonics according to their respective Fourier series analyses. This representation allows better performance of the model, whose capability to generate gait information is validated through experiments using a real active orthotic device, analysing both joint motor energy consumption and user metabolic effort.

Online trajectory generation for wide ditch crossing of biped robots using control constraints

This work proposes a multibody dynamics approach to generate joint trajectories for a five degrees of freedom biped robot crossing a wide ditch whose width is greater than or equal to the robot’s leg length. Trajectories are generated using control constraints that depend on the horizontal distance traveled by the center of mass and are not explicitly dependent on time. Behavior of the biped robot for various initial postures is studied considering dynamic balance, friction, and impact in order to find the preferred initial postures considering the net energy consumption and peak power requirements at various joints. Several cases of friction, zero moment point location, and the center of mass height variation are considered in the study. Using the proposed approach, feasible trajectories for an adult sized biped robot could be generated for a wide ditch of 1.05 m width at coefficients of friction as low as 0.2. The results obtained are useful for designing reference trajectories and actuation systems for biped robots that need to cross wide ditches or take large steps. Time needed for trajectory generation is found to be sufficiently low for online implementation.

Robot motion synthesis using ground reaction forces pattern

Gait generation in its realization stage in majority of bipeds involves inverse dynamics model with the need of pre-determined joint trajectories and the zero moment point method for final postural stability adjustments. This requires generation of such joint trajectories, where the zero moment point criterion is fulfilled and the human-like posture is kept. Such task is complex and still misses the universal solution. Preserving natural (human-like) and stable body posture under acting disturbances is an issue too. High computational costs, problem with disturbances rejection and controller complexity are the major disadvantages associated with such approaches. This article presents a method for motion control with forward dynamics model and ground reaction forces as the reference values. The ground reaction forces measured during real human walking are utilized here. A MATLAB/Simulink framework is used for testing the proposed synthesis of bipedal locomotion. The ground reaction forces recorded during the walk with different footwear are applied as the references. The obtained motion patterns and postures are compared with those of the human. Obtained results were satisfactory and justified the proposed approach.

Generation and optimal choice of joint trajectories using all solutions of inverse kinematics of general 6-R robots

ABSTRACTIn this article, an algorithm is presented that transforms a given trajectory of a general 6-R Robot in Cartesian task space (position and orientation) into all possible joint space trajectories. It is shown how all solutions of the inverse kinematics can be used to obtain continuous joint trajectories. Inverse kinematics yields up to 16 different solution paths in joint space and these joint paths are compared using different optimality criteria. To achieve this goal the Cartesian trajectory is discretized and at each instant the inverse kinematics is computed using a fast algorithm developed in Pfurner and Husty et al. In the set of joint angles corresponding to the inverse kinematics solutions coherent paths are determined and interpolated with quintic splines. Different boundary conditions for the construction of the splines are discussed. Using the splines some possibilities for the optimal choice among the paths using different criteria are presented.

A novel approach to gait synchronization and transition for reconfigurable walking platforms

Legged robots based on one degree-of-freedom reconfigurable planar leg mechanisms, that are capable of generating multiple useful gaits, are highly desired due to the possibility of handling environments and tasks of high complexity while maintaining simple control schemes. An essential consideration in these reconfigurable legged robots is to attain stability in motion, at rest as well as while transforming from one configuration to another with the minimum number of legs as long as the full range of their walking patterns, resulting from the different gait cycles of their legs, is achieved. To this end, in this paper, we present a method for the generation of input joint trajectories to properly synchronize the movement of quadruped robots with reconfigurable legs. The approach is exemplified in a four-legged robot with reconfigurable Jansen legs capable of generating up to six useful different gait cycles. The proposed technique is validated through simulated results that show the platform׳s stability across its six feasible walking patterns and during gait transition phases, thus considerably extending the capabilities of the non-reconfigurable design.

Speed-dependent reference joint trajectory generation for robotic gait support

For the control of actuated orthoses, or gait rehabilitation robotics, kinematic reference trajectories are often required. These trajectories, consisting of joint angles, angular velocities and accelerations, are highly dependent on walking-speed. We present and evaluate a novel method to reconstruct body-height and speed-dependent joint trajectories. First, we collected gait kinematics in fifteen healthy (middle) aged subjects (47–68), at a wide range of walking-speeds (0.5–5kph). For each joint trajectory multiple key-events were selected (among which its extremes). Second, we derived regression-models that predict the timing, angle, angular velocity and acceleration for each key-event, based on walking-speed and the subject׳s body-height. Finally, quintic splines were fitted between the predicted key-events to reconstruct a full gait cycle. Regression-models were obtained for hip ab-/adduction, hip flexion/extension, knee flexion/extension and ankle plantar-/dorsiflexion. Results showed that the majority of the key-events were dependent on walking-speed, both in terms of timing and amplitude, whereas the body-height had less effect. The reconstructed trajectories matched the measured trajectories very well, in terms of angle, angular velocity and acceleration. For the angles the RMSE between the reconstructed and measured trajectories was 2.6°. The mean correlation coefficient between the reconstructed and measured angular trajectories was 0.91. The method and the data presented in this paper can be used to generate speed-dependent gait patterns. These patterns can be used for the control of several robotic gait applications. Alternatively they can assist the assessment of pathological gait, where they can serve as a reference for “normal” gait.

Online Joint Trajectory Generation of Human-like Biped Walking

Biped walking has long been studied in the area of gait analysis and robotic locomotion. The goal of this paper is to establish a systematic methodology for human-like natural walking by fusing the measured human joint data and optimal pattern generation techniques based on a full-body humanoid model. To this end, this paper proposes an adaptive two-stage gait pattern by which the step length and walking velocity can be changed with two scaling factors. In addition, to cope with the situations involving passing over a small obstacle, the joint trajectories of the swing foot can be adjusted with a novel concept of differential angle trajectory using a reliable optimization method, viz. particle swarm optimization. The feasibility of the proposed walking scheme is validated by walking experiments with the robot platform DARwIn-OP.

A Comparative Study among Three Automatic Gait Generation Methods for Quadruped Robots

This paper introduces a comparison of three automatic gait generation methods for quadruped robots: GA (Genetic Algorithm), GP (genetic programming) and CPG (Central Pattern Generator). It aims to provide a useful guideline for the selection of gait generation methods. GA-based approaches seek to optimize paw locus in Cartesian space. GP-based techniques generate joint trajectories using regression polynomials. The CPGs are neural circuits that generate oscillatory output from an input coming from the brain. Optimizations for the three proposed methods are executed and analyzed using a Webots simulation of the quadruped robot built by Bioloid. The experimental comparisons and analyses provided herein will be an informative guidance for research of gait generation method.

Generation of Minimal Energy Joint Trajectories during Single Support Phase for 3-dimensional Bipedal Walking

Generation of Minimal Energy Joint Trajectories during Single Support Phase for 3-dimensional Bipedal Walking

Time-optimal and Jerk-continuous Trajectory Planning Algorithm for Manipulators

In order to optimize the productivity and ensure the running stability of manipulators, a new optimal trajectory planning algorithm is proposed. Position series in joint space are obtained by applying inverse kinematic algorithm to a specified trajectory in task space, and B-splines of seven degree are exploited to interpolate joint position series and generate joint trajectories with continuous velocity, acceleration and jerk, as well as controllable start-stop kinematic parameters. By converting kinematic constraints of manipulators to constraints on control points of B-splines, optimal time nodes are solved by using sequential quadratic programming strategy, then time-optimal and jerk-continuous trajectories which satisfy nonlinear kinematic constraints are planned. Simulating and experimental results show that the proposed trajectory planning algorithm provides ideal trajectories for joint controller, and ensures manipulators to track any specified trajectory in task space stably with the minimum traveling time.

Three-dimensional modelling of a humanoid in three planes and a motion scheme of biped turning in standing

The rigorous three-dimensional model of a humanoid is essential for biped walking, turning, carrying and the like. This study presents a new three-dimensional model of a humanoid by adding two joints in the transverse plane for enabling the motion of turning. Using this model, the authors propose a motion scheme for turning the forward direction of a humanoid in standing. In the present work, every component motion carried out per plane is separately illustrated with figures and explanations. Then, a right-hand turning of a humanoid in standing is simulated and implemented with a small humanoid robot for validation. The present work will serve as a foundation for joint trajectory generation about complex three-dimensional motions of a humanoid robot.

An Alternate Control Strategy of a Mobile Manipulator With Hardware and Software Description

Abstract This paper presents an approach for desired joint trajectory generation for motion control of a mobile manipulator. The objective is to allow the end-effector tracks a given operational trajectory in a fixed world frame. In this paper, each of the arm and the mobile platform is treated separately. This mode of operation is well suited in simple manipulation tasks like pick and place. We also present the hardware architecture, which makes use of a PC as the host. It is configured in such a way that it performs all the input-output interface operations. On the other hand, we have implemented a low level layer that includes the required hardware for each of the sub-systems making the mobile manipulator. The results presented have tested and showed the effectiveness of the method for tasks like pick and plac

Trajectory Planning for the Walking Biped “Lucy”

A real-time joint trajectory generator for planar walking bipeds is proposed. In the near future this trajectory planner will be implemented on the robot “Lucy”, which is actuated by pleated pneumatic artificial muscles. The trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the strategy developed is demonstrated by simulation results. A first simulation is performed under the assumption of perfect tracking by the controllers of the different actuators. This allows one to verify the effectiveness of the trajectory planner and to evaluate the postural stability. A second simulation is performed while taking the control architecture of the real robot into account. In order to have a more realistic simulation the proposed control architecture is evaluated with a full hybrid dynamic simulation model of the biped “Lucy”. This simulator combines the dynamical behaviour of the robot with the thermodynamical effects that take place in the muscle-valves actuation system. The observed hardware limitations of the real robot and expected model errors are taken into account in order to give a realistic qualitative evaluation of the control performance and to test the robustness.

Controlling a bipedal walking robot actuated by pleated pneumatic artificial muscles

This paper reports on the control structure of the pneumatic biped Lucy. The robot is actuated with pleated pneumatic artificial muscles, which have interesting characteristics that can be exploited for legged locomotion. They have a high power to weight ratio, an adaptable compliance and they can absorb impact effects.The discussion of the control architecture focuses on the joint trajectory generator and the joint trajectory tracking controller. The trajectory generator calculates trajectories represented by polynomials based on objective locomotion parameters, which are average forward speed, step length, step height and intermediate foot lift. The joint trajectory tracking controller is divided in three parts: a computed torque module, a delta-p unit and a bang-bang pressure controller. The control design is formulated for the single support and double support phase, where specifically the trajectory generator and the computed torque differs for these two phases.The first results of the incorporation of this control architecture in the real biped Lucy are given. Several essential graphs, such as pressure courses, are discussed and the effectiveness of the proposed algorithm is shown by the small deviations between desired and actual attained objective locomotion parameters.