A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

Evaluation of the Radial Procurvatum Using the Center of Rotation of Angulation Methodology in Chondrodystrophic Dogs

The radial joint orientation angles were calculated using the center of rotation of angulation (CORA) methodology within the frontal and sagittal planes in chondrodystrophic dog breeds, including Welsh Corgi, Dachshund, Pekinese, Poodle, Beagle and Maltese, and it was compared whether there is a statistically significant difference between the breeds. Radial joint orientation angles were obtained in eighty-eight dogs, including 23 Welsh Corgis, 16 Dachshunds, 14 Pekinese, 13 Maltese, 12 Poodles and 10 Beagles. Using the CORA methodology, the cranial proximal radial angle (CrPRA) and caudal distal radial angle (CdDRA) in the sagittal plane and medial proximal radial angle (MPRA) and lateral distal radial angle (LDRA) in the frontal plane were measured for the six breeds studied. The mean values of joint angles for each breed were compared statistically were observed. The CrPRA, CdDRA, and LDRA mean values of Dachshund and Welsh Corgi breeds were significantly smaller than other breeds, and in MPRA, Pekingese showed significantly smaller values than other breeds. This study confirms that the mean values of radial joint orientation angles can be significantly different among chondrodystrophic breeds. To accurately evaluate the degree of angular deformity of the radius, it may be helpful to refer to the average value for each breed with chondrodystrophy.

Sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for reaction motion

With the wide application of redundant manipulators, sharing a working space with humans and dealing with uncertainty seems an inevitable problem, especially in the dynamic and unstructured domain. How to deal with obstacle avoidance is of particular importance that robots and humans/environments are safe interactions to fulfill the complex cooperating tasks. This paper aimed at solving the problem of multiple points avoidance for the reaction motion based on the skeleton algorithm in unstructured and dynamic environments. A method named “sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for the reaction motion” is proposed. The extraction of skeleton information from image is obtained to calculate the distances of the multiple control points and establish the repulsion in this method. Afterward, the force Jacobian related to the priority weighting factors is calculated and then a reaction force with damping term is established, which is corresponding nominal torque commands. For the redundant manipulator, the joint angles are obtained through torque iteration instead of inverse kinematics to reduce calculation cost. Finally, the method was tested by a 7-DOF manipulator in the ROS framework. The obtained results indicate that the method in this method can realize dynamic obstacle avoidance and time cost reduction.

Investigating the Effect of Real-Time Center of Pressure (CoP) Feedback Training on the Swing Phase of Lower Limb Kinematics in Transfemoral Prostheses with SACH foot

Transfemoral amputee often encounters reduced toe clearance resulting in trip-related falls. Swing phase joint angles have been shown to influence the toe clearance therefore, training intervention that targets shaping the swing phase joint angles can potentially enhance toe clearance. The focus of this study was to investigate the effect of the shift in the location of the center of pressure (CoP) during heel strike on modulation of the swing phase joint angles in able-bodied participants (n=6) and transfemoral amputees (n=3). We first developed a real-time CoP-based visual feedback system such that participants could shift the CoP during treadmill walking. Next, the kinematic data were collected during two different walking sessions- baseline (without feedback) and feedback (shifting the CoP anteriorly/posteriorly at heel strike to match the target CoP location). Primary swing phase joint angle adaptations were observed with feedback such that during the mid-swing phase, posterior CoP shift feedback significantly increases (p<0.05) the average hip and knee flexion angle by 11.55 degrees and 11.86 degrees respectively in amputees, whereas a significant increase (p<0.05) in ankle dorsiflexion, hip and knee flexion angle by 3.60 degrees, 3.22 degrees, and 1.27 degrees respectively compared to baseline was observed in able-bodied participants. Moreover, an opposite kinematic adaptation was seen during anterior CoP shift feedback. Overall, results confirm a direct correlation between the CoP shift and the modulation in the swing phase lower limb joint angles.

A numerically stable algorithm for analytic inverse kinematics of 7-DoF S-R-S manipulators with joint limit avoidance

This paper presents a numerically stable algorithm for analytic inverse kinematics of 7-DoF S-R-S manipulators with joint limit avoidance. The arm angle is used to represent the self-motion manifold within a global arm configuration. The joint limits are analytically mapped to the arm angle space for joint limit avoidance. To profile the relation between the joint angle and arm angle, it is critical to characterize the singular arm angle for each joint. In the-state-of-the art methods, the existence of the singular arm angle is triggered by comparing a discriminant with zero given a threshold. We will show this leads to numerical issues since the threshold is inconsistent among different target poses, leading to incorrect range of the arm angle. These issues are overcome by associating indeterminate joint angles of tangent joints with angles of 0 or pi of cosine joints, rather than using an independent threshold for each joint. The closed-form algorithm in C++ code to perform numerically stable inverse kinematics of 7-DoF S-R-S manipulators with global arm configuration control and joint limit avoidance is also given.

Improved 3D Human Motion Capture Using Kinect Skeleton and Depth Sensor

Kinect has been utilized as a cost-effective, easy-to-use motion capture sensor using the Kinect skeleton algorithm. However, a limited number of landmarks and inaccuracies in tracking the landmarks’ positions restrict Kinect’s capability. In order to increase the accuracy of motion capturing using Kinect, joint use of the Kinect skeleton algorithm and Kinect-based marker tracking was applied to track the 3D coordinates of multiple landmarks on human. The motion’s kinematic parameters were calculated using the landmarks’ positions by applying the joint constraints and inverse kinematics techniques. The accuracy of the proposed method and OptiTrack (NaturalPoint, Inc., USA) was evaluated in capturing the joint angles of a humanoid (as ground truth) in a walking test. In order to evaluate the accuracy of the proposed method in capturing the kinematic parameters of a human, lower body joint angles of five healthy subjects were extracted using a Kinect, and the results were compared to Perception Neuron (Noitom Ltd., China) and OptiTrack data during ten gait trials. The absolute agreement and consistency between each optical system and the robot data in the robot test and between each motion capture system and OptiTrack data in the human gait test were determined using intraclass correlations coefficients (ICC3). The reproducibility between systems was evaluated using Lin’s concordance correlation coefficient (CCC). The correlation coefficients with 95% confidence intervals (95%CI) were interpreted substantial for both OptiTrack and proposed method (ICC > 0.75 and CCC > 0.95) in humanoid test. The results of the human gait experiments demonstrated the advantage of the proposed method (ICC > 0.75 and RMSE = 1.1460°) over the Kinect skeleton model (ICC < 0.4 and RMSE = 6.5843°).

Human Gait Data Augmentation and Trajectory Prediction for Lower-Limb Rehabilitation Robot Control Using GANs and Attention Mechanism

To date, several alterations in the gait pattern can be treated through rehabilitative approaches and robot assisted therapy (RAT). Gait data and gait trajectories are essential in specific exoskeleton control strategies. Nevertheless, the scarcity of human gait data due to the high cost of data collection or privacy concerns can hinder the performance of controllers or models. This paper thus first creates a GANs-based (Generative Adversarial Networks) data augmentation method to generate synthetic human gait data while still retaining the dynamics of the real gait data. Then, both the real collected and the synthesized gait data are fed to our constructed two-stage attention model for gait trajectories prediction. The real human gait data are collected with the five healthy subjects recruited from an optical motion capture platform. Experimental results indicate that the created GANs-based data augmentation model can synthesize realistic-looking multi-dimensional human gait data. Also, the two-stage attention model performs better compared with the LSTM model; the attention mechanism shows a higher capacity of learning dependencies between the historical gait data to accurately predict the current values of the hip joint angles and knee joint angles in the gait trajectory. The predicted gait trajectories depending on the historical gait data can be further used for gait trajectory tracking strategies.