Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> A method is presented for the generation of a free gait for the straight-line motion of a quadruped walking machine. It uses a heuristic graph search procedure based on the A* algorithm. The method essentially looks into the consequences of a move to a certain depth before actually committing to it. Deadlocks and inefficiencies are thus sensed well in advance and avoided. > <s> BIB001 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> Selecting an appropriate gait can reduce consumed energy by a biped robot. In this paper, a Genetic Algorithm gait synthesis method is proposed, which generates the angle trajectories based on the minimum consumed energy and minimum torque change. The gait synthesis is considered for two cases: walking and going up-stairs. The proposed method can be applied for a wide range of step lengths and step times during walking; or step lengths, stair heights and step times for going up-stairs. The angle trajectories are generated without neglecting the stability of the biped robot. The angle trajectories can be generated for other tasks to be performed by the biped robot, like going down-stairs, overcoming obstacles, etc. In order to verify the effectiveness of the proposed method, the results for minimum consumed energy and minimum torque change are compared. A Radial Basis Function Neural Network is considered for the real-time application. Simulations are realized based upon the parameters of the 'Bonten-Maru ... <s> BIB002 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> Abstract As autonomous humanoid robots assume more important roles in everyday life, they are expected to perform many different tasks and quickly adapt to unknown environments. Therefore, humanoid robots must generate quickly the appropriate gait based on information received from visual system. In this work, we present a new method for real time gait generation during walking based on Neural Networks. The minimum consumed energy gaits similar with human motion, are used to teach the Neural Network. After supervised learning, the Neural Network can quickly generate the humanoid robot gait. Simulation and experimental results utilizing the “Bonten-Maru I” humanoid robot show good performance of the proposed method. <s> BIB003 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> In this paper we present the experimental validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N -link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints—holonomic constraints imposed via feedback—on the robot’s configuration, which create an attracting two-dimensional invariant set in the full walking model’s state space. Stability properties of resulting walking motions are easily analyzed in terms of a two-dimensional subdynamic of the full walking model. A practical introduction to and interpretation of the framework is given. In addition, in this paper we develop the ability to regulate the average walking rate of the biped to a continuum of values by modification of within-stride and stride-boundary characteristics, such as step length. <s> BIB004 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> This paper is devoted to a stability study of a walking gait for a biped. The walking gait is periodic and it is composed of a single-support phase, a passive impact, and a double-support phase. The reference trajectories are described as a function of the shin orientation versus the ground of the stance leg. We use the Poincare map to study the stability of the walking gait of the biped. We only study the stability of dynamics not controlled during the single-support phase, i.e., the dynamics of the shin angle. We then suppose there is no perturbation in the tracking of the references of the other joint angles of the biped. The studied Poincare map is then of dimension one. With a particular control law in double support, it is shown theoretically and in simulation that a perturbation error in the velocity of the shin angle can be eliminated in one step only. The zone of convergence in one step is determined. The condition of existence of a cyclic gait is given, and for a given cyclic gait, the stability condition is also given. It is shown that due to the given control law for the overactuated double-support phase, a cyclic motion is practically guaranteed to be stable. It should be noted it is possible for the biped to reach a periodic regime from a stopped position in one step. <s> BIB005 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C3fitted at knots uniformly distributed along the motion time. This high-order differentiability eliminates jerky variations of actuating torques. Through connecting conditions, spline polynomial coefficients are determined as a linear function of the joint coordinates at knots. These values are then dealt with as optimization parameters. An optimal control problem is formulated on the basis of a performance criterion to be minimized, representing an integral quadratic amount of driving torques. Using the above spline approximations, this primary problem is recast into a constrained non-linear optimization problem of mathematical programming, which is solved using a computing code implementing an SQP algorithm. As numerical simulations, complete gait cycles are generated for a seven-link planar biped. The only kinematic data to be accounted for are the walking speeds. Optimization of both phases of gait is carried out globally; it includes the optimization of transition configurations of the biped between successive phases of the gait cycle. <s> BIB006 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> This paper presents the virtual height inverted pendulum mode (VHIPM), which is a simple and effective trajectory generation method for the stable walking of biped robots. VHIPM, which is based on the inverted pendulum mode (IPM), can significantly reduce the zero moment point (ZMP) error by adjusting the height in the inverted pendulum. We show the relationship between VHIPM and other popular trajectory generation methods, and compare the ZMP errors in walking when trajectories are generated by various methods including VHIPM. We also investigate the sensitivity of the ZMP error in VHIPM to the step length, walking period and mass distribution of a robot. The simulation results show that VHIPM significantly reduces the ZMP errors compared to other methods under various circumstances. <s> BIB007 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> The development of optimized motions of humanoid robots that guarantee fast and also stable walking is an important task, especially in the context of autonomous soccer-playing robots in RoboCup. We present a walking motion optimization approach for the humanoid robot prototype HR18 which is equipped with a low-dimensional parameterized walking trajectory generator, joint motor controller and an internal stabilization. The robot is included as hardware-in-the-loop to define a low-dimensional black-box optimization problem. In contrast to previously performed walking optimization approaches, we apply a sequential surrogate optimization approach using stochastic approximation of the underlying objective function and sequential quadratic programming to search for a fast and stable walking motion. This is done under the conditions that only a small number of physical walking experiments should have to be carried out during the online optimization process. For the identified walking motion for the considered 55 cm tall humanoid robot, we measured a forward walking speed of more than 30 cm s-1 . With a modified version of the robot, even more than 40 cm s-1 could be achieved in permanent operation. <s> BIB008 </s> Intelligent Approaches in Locomotion - A Review <s> Optimisation <s> This paper presents an algorithm for planning the foothold positions of quadruped robots on irregular terrain. The input to the algorithm is the robot kinematics, the terrain geometry, a required motion path, as well as initial posture. Our goal is to develop general algorithm that navigate quadruped robots quasi-statically over rough terrain, using an APF (Artificial Potential Field) and graph searching. The algorithm is planning a sequence set of footholds that navigates the robot along the required path with controllable motion characteristics. Simulations results demonstrate the algorithm in a planner environment. <s> BIB009
The specification of gait form and the use of conservative stability constraints usually limit the optimisation scope. However, there are some parameters available to adjust, e.g., gait parameters including stride length and cycle frequency. These parameters can therefore be candidates for optimisation, according to some desired goal. Such optimisation goals have included minimisation of energy expenditure BIB005 ,  , BIB004 , BIB002 - BIB003 , minimisation of actuating effort BIB006 ,  , improved form through minimisation of ZMP error BIB007 , stability  , BIB004 , speed expressed as maximum distance over a set time frame BIB008 , minimisation of speed error  . For those systems, which are lightly constrained in the analysis, constraints are imposed during optimisation to ensure walking gaits are formed  . Energy and effort goals are important due to difficulties in realising robots in the real world. Reducing the energy requirements makes robots more practical, and form and speed goals address their functionality. Minimising actuating effort, defined as the integral square of actuator torques, instead of simple energy minimisation, was done for two reasons in BIB006 . Firstly, the quadratic nature of the fitness function favours smooth continuous actuator changes, which compares to actuator discontinuities that can result from energy minimisation. Secondly, an upright pattern was favoured, as it required only small torques to maintain. The parameters for optimisation can be arbitrary constants, or they may have a direct interpretation. To have direct interpretation, the equations have to explicitly use understandable variables. This may require extra analytical work or result in more constrained solutions. Arbitrary parameters were specified in BIB007 , BIB005 , BIB006 - BIB004 , BIB008 ,  . In contrast, specific end and intermediate target points of the gait were specified by optimisation in BIB002 - BIB003 . Various techniques have been used for optimisation, including Genetic Algorithms (GA) in BIB002 - BIB003 , sequential surrogate optimisation (which works on an approximation of the objective function in order to speed up the optimisation -useful for real world cases) BIB008 , sequential quadratic programming BIB006 - BIB004 , and simple error based feedback BIB007 . For the velocity error minimisation problem in  , the complicated algorithms derived in analysis were better optimized with random search when compared to gradient and sequential searches, due to numerical stability issues. In BIB009 a Depth First Search algorithm was used to plan the movement of a hexapod's legs in order to navigate along a path, and in BIB001 an A* search algorithm was used for similar reasons.