El acta 1 Definición

Human posture prediction typically involves finding a set of joint rotations and translations that results in an end-effector reaching a given target point in Cartesian space. Before a review of this problem is given, it is necessary to briefly describe the basic computational procedures used in human posture modelling, which are forward kinematics and inverse kinematics. Forward kinematics refers to the procedure of computing joint and end-effector (e.g., fingertip) coordinates from known joint or segmental angles. Inverse kinematics is the procedure of determining the joint or segmental angle from known joint coordinates, or most often end-effector coordinates. In biomechanical models of human posture, normally the number of joint angles (i.e. degrees of freedom) is greater than the dimension of end-effector position. Therefore, kinematic redundancy in inverse kinematics occurs, which gives rise to a very fundamental problem in the modelling of human posture – the so-called Bernstein’s problem.

There are two approaches to solve the posture prediction problem. The first and the more traditional one is to use the classical animation obtained from experiments or user-manipulation of manikins. Firstly, data is collected either from thousands of experiments with human subjects, or from simulations with 3D human modelling software. Then, the data is analysed statistically to form predictive posture models (e.g., regression models). These models have been implemented in simulation software tools along with various methods in order to select the most probable posture given in a specific scenario [41–43]. Although this approach is based on actual human data thus does not need to be verified in terms of realism, it involves a time-consuming data collection process often requiring thousands of human subjects.

Another approach for solving posture prediction problem is based on optimisation where various performance measures served as objective functions or cost functions are formulated to mathematically represent an optimal strategy in determining joint motions. It hypothesises that human performances govern human posture; thus the process of human posture simulation can be formulated as an optimisation problem that minimises human performance measures given at different constraints and hand loads, corresponding to a number of manual tasks. Zhao and Badler used constrained, gradient-based optimisation to minimise an objective function formed by weighted sum of components which model various factors, such as the position of the fingers (end-effector) or the orientation of the hands [44]. Limits on the joint angles were incorporated as constraints. Riffard and Chedmail used an unconstrained global optimisation approach in order to determine the optimum placement of the torso and the optimum posture of a 7 degree-of-freedoms arm [45]. Equations for target contact, collision avoidance, vision, body-orientation and torque were combined in a weighted sum to form the objective function. In addition, coupling between particular joint angles and variable joint limits was modelled. The final unconstrained problem was solved using simulated annealing, nonetheless the solution process was relatively slow. Yu used the same fundamental approach but took joint displacement and potential energy as objective functions for a 3 degree-of-freedoms arm [46]. The problem was solved using a genetic algorithm, which is also a relatively slow global optimisation technique. Mi extended the work of Yu to a 15 degree-of-freedoms arm [47]. A real-time optimisation algorithm was developed which combines predetermined genetic algorithm results with an unconstrained gradient-based algorithm.

In optimisation-based approaches, the idea of combining multiple objective functions to determine an optimal solution leads the application of multi-objective optimisation (MOO) method. Zhao and Bai used MOO method to solve problems of load distribution and joint trajectory planning, taking the minimum joint or/and load as objective functions [48]. With respect to robot motion prediction, Saramago and Steffen used this method to minimise the travel time for a robot and the mechanical energy of robotic actuators, considering dynamics and collision avoidance of moving obstacles [49, 50]. With respect to human posture prediction, Yang et al. described the use of MOO method to predict human’s upper body posture, combining joint displacement, potential energy and discomfort as human performance measures [51, 52]. Ma et al. proposed the use of MOO to predict and analyse the human posture with the

consideration of physical fatigue and joint discomfort concurrently [53]. These studies adopted a weighted sum method to convert the multiple objectives into a single objective to achieve the Pareto optimal sets of the optimisation problem and then investigated the effect of various weighting factors to Pareto optimal set in order to obtain the insight of the most desirable manner to combine multiple objectives.

The accuracy of optimisation-based posture prediction is heavily dependent on the objective function. Hence there is a potential development not only within the optimisation algorithm but also within the human performance measures. In addition, inverse kinematics algorithm is not necessarily correct for perdition of posture because its theoretical foundation may violate task constraints. Therefore, the development and integration of task constraints modelled from specific task contexts into posture prediction is essential when posture-prediction approach continues to advance.