Aerial robot technologies, such as drones and unmanned aerial vehicles, are rapidly advancing in various domains. These robots now possess enhanced autonomous flying abilities and use sensor technology, Global Navigation Satellite System (GNSS), Light Detection and Ranging (LiDAR) system, and cameras to avoid obstacles, automatically land, and track flights. Evolving technologies in airspace management and route optimization ensure that flights are efficient and safe. Aerial robots have a wide range of applications, such as agriculture, disaster response, environmental monitoring, and inspection. These devices excel at precise data collection thanks to their high-resolution cameras and high-precision sensors. Swarm robotics, which allows collaboration between multiple aerial and ground robots, is also progressing. This enables quick coverage of large areas, which benefits disaster relief and land management. In addition, research and development of flying robots modeled after flying animals is underway. The evolution of aerial robots results in their efficient use in a variety of fields and new applications.

This special issue includes the latest research papers and development reports on aerial robotic technology from the aforementioned perspectives. We hope that this special issue will pique researchers’ and engineers’ interest in aerial robots, thereby encouraging additional research and development. Finally, we would like to express our gratitude to all authors, all reviewers, the editorial board of the Journal of Robotics and Mechatronics, and Fuji Technology Press Ltd.

This paper proposes a method for generating highly accurate point cloud maps of orchards using an unmanned aerial vehicle (UAV) equipped with light detection and ranging (LiDAR). The point cloud captured by the UAV-LiDAR was converted to a geographic coordinate system using a global navigation satellite system / inertial measurement unit (GNSS/IMU). The converted point cloud is then aligned with the simultaneous localization and mapping (SLAM) technique. As a result, a 3D model of an orchard is generated in a low-cost and easy-to-use manner for pesticide application with precision. The method of direct point cloud alignment with real-time kinematic-global navigation satellite system (RTK-GNSS) had a root mean square error (RMSE) of 42 cm between the predicted and true crop height values, primarily due to the effects of GNSS multipath and vibration of automated vehicles. Contrastingly, our method demonstrated better results, with RMSE of 5.43 cm and 2.14 cm in the vertical and horizontal axes, respectively. The proposed method for predicting crop location successfully achieved the required accuracy of less than 1 m with errors not exceeding 30 cm in the geographic coordinate system.

In recent years, the application of bio-inspired structures has garnered attention for enhancing the performance of fluid machinery. In this study, we experimentally investigated the effects of introducing a bio-inspired cutout structure to the propellers of drones, aiming to improve thrust efficiency and reduce noise levels. Our results demonstrated reductions in noise levels compared to conventional propellers. Parametric studies revealed that the roundness of the structure significantly influenced both flight efficiency and noise levels, suggesting its importance for replicating the inherent fluid characteristics found in nature. Additionally, optimal parameters for noise reduction, such as the length of the cutout, angle of incision relative to the flow direction, and the distance between the gap were identified. Although no improvements in flight efficiency were observed, most of the models investigated exhibited only around a 5% reduction in efficiency compared to the standard propellers, suggesting practical applicability for scenarios such as nighttime drone operations in urban areas. The noteworthy reduction in sound pressure levels in the mid- to high-frequency range achieved by the bio-inspired propellers in this study holds the potential to address the issue of drone noise pollution and encourage drone operations in urban areas. Moreover, the confirmed decrease in sound pressure at specific frequencies and the suggested controllability hint at the possibility of enhancing sound source localization performance using drones.

In Japan today, aging infrastructures such as dams and bridges are becoming an issue. We considered that the use of a hydrofoil multicopter would be an effective method for inspecting and surveying such facilities. When using a hydrofoil multicopter, it is possible to take off from the shore, land on the water, and dive without using a ship. The aircraft developed in this study has the capability to communicate with the land. The aircraft developed in this study is equipped with a communication buoy, and after landing on the water, a communication cable is extended from the buoy to enable underwater maneuvering via wired communication. We report on the development of a precise control system for flight and diving of this aircraft.

In this study, we developed a docking mechanism for drones that enables docking and undocking in the air for cargo transportation. This capability allows the drone configuration to be adapted depending on the cargo size and shape. We introduced a novel docking mechanism that incorporates magnetic adsorption and a newly engineered locking mechanism. We developed a drone detection system capable of estimating the relative position of a target drone by utilizing an onboard camera to identify the infrared LEDs on the target drone via image processing. Moreover, flight experiments, including detection, docking, and undocking, were performed using a mock drone to demonstrate the effectiveness of the developed system.

In this study, we propose a novel tailsitter unmanned aerial vehicle with configurable wings using a parallel link mechanism. It has two flight modes: a hover mode and a forward flight mode by pitching, similar to conventional tailsitters. In addition, it can deform its airframe in each flight mode. In the hover mode, it can tilt the frame in the pitch direction while hovering. In the forward flight mode, it can change the configuration of the wings during forward flight. In experiments, we show that it can transition from the hover mode to the forward flight mode with three wing configurations: non-staggered wings (biplane) and positively and negatively staggered wings (tandem wing plane), using an attitude controller for conventional quadrotors.

In this study, we investigated inspection robots that can safely, accurately, and quickly perform hammer sound inspections on tile exterior walls and present new wall hammering inspection systems using two-wheeled multi-copters. Our results yielded the following five advantages. First, the proposed multi-copter can use its wheels not only to move freely on the walls of buildings but also to overcome obstacles on the walls. Therefore, almost any tile wall surface can be inspected for hammering sound. Second, the multi-copter was equipped with both hammer-shaped rods to hit the tile exterior wall and microphones to collect the hammer sound of the tile, while moving quickly on the wall surface. Third, the wall hammering inspection systems can be used safely with a work assistance mechanism using a wire even in densely populated areas, such as urban areas, because the multi-copter has high wind resistance against crosswinds by both pushing against the wall and operating by the wire. Fourth, we presented some automatic control systems that make the multi-copter operation easy during hammering inspections and demonstrated its usefulness through experiments. Fifth, we proposed useful methods for detecting floating tiles based on the hammering results, conducted some outdoor flight experiments on building exterior walls, and demonstrated that floating tiles can be determined with high accuracy.

In recent years, Japan has experienced numerous natural disasters, such as typhoons and earthquakes. Teleoperated ground robots (including construction equipment) are effective tools for restoration work at disaster sites and other locations that are dangerous and inaccessible to humans. Using visual information obtained from various viewpoints by a drone can allow for more effective remote control of a teleoperated ground robot, making it easier for the robot to perform a task. We previously proposed and developed a remote-controlled drone system using only human eyes. However, the effectiveness of using this drone system during the remote control of a robot has never been verified. In this paper, as the first step in verifying the effectiveness of the remote-controlled drone system using only the eyes when remote-controlling a robot, we consider its effectiveness in a simple task based on the task times, subjects’ eye fatigue, and subjective evaluations of subjects. First, the previously proposed drone system is briefly described. Next, we describe an experiment in which a drone was controlled by the eyes using the drone system while a robot was controlled by hand, and an experiment in which both the drone and robot were controlled by hand without using the drone system. Based on the experimental results, we evaluate the effectiveness of the remote-controlled drone system using only the eyes when remote-controlling a robot.

This study investigates a method for generating obstacle avoidance trajectories for arbitrary convex polyhedrons. We propose a formulation that converts discrete conditions into continuous equation forms to avoid convex polyhedron obstacles. The condition that the evaluation point be located outside of the convex polyhedron can be transformed into a constraint in the continuous equation form and incorporated into the optimization calculation to generate avoidance trajectories. Avoidance trajectory generation using the Legendre pseudospectral method is performed for convex polyhedral obstacles of various shapes. The results show that the proposed method successfully generates avoidance trajectories for arbitrary convex polyhedral obstacles.

This study applies a successful collision-avoidance method using buffered Voronoi cells (BVC) to control quadrotors. In particular, we consider the case of dealing with stationary obstacles using only the local information obtained from sensors, which has not been discussed in previous studies. In this study, we assume an unknown environment with grid-shaped obstacles. We demonstrate that four quadrotors can compute the information required for the BVC-based collision avoidance algorithm and move in the same environment without communicating with each other or receiving information from a central controller, using the local information obtained from the mounted 3D LiDAR. Simulations indicate that the system can handle static obstacles using point-cloud data obtained using 3D LiDAR as Voronoi seeds. We also demonstrate that the BVC-based collision avoidance algorithm can be applied to quadrotors controlled by a simple PD position controller without any modification to the controller. These findings show that the BVC-based collision avoidance can be easily implemented using existing commercial drones.

Uncrewed aircraft systems and advanced air mobility are associated with uncertain conditions, such as wind prediction errors, and they may deviate from dedicated airspaces referred to as corridors. However, further studies on these aspects are required. This study focuses on the covariance control for a stochastic discrete-time linear system under correlated uncertainties. A covariance control problem with chance constraints can be formulated as a convex-programming problem. Numerical simulations of uncrewed aircraft systems path planning can be used to compare two control laws: covariance control laws that consider correlated and noncorrelated noise. Numerical simulations were conducted to verify that the covariance control law considering correlated noise generates a trajectory that appropriately satisfies the constraints. Consequently, the effect of considering correlated noise in the covariance control law was clarified. In addition, covariance control has been demonstrated to generate appropriate trajectories for various state constraints. Moreover, numerical simulations indicated that covariance control facilitated the control of uncertainty, and the effectiveness of the covariance control was evaluated. The insights gained from the results of this study can inform enhanced uncertainty management for improving reliability and safety in real-world applications of uncrewed aircraft systems and advanced air mobility.

Last-mile delivery systems are one of the numerous industrial applications of uncrewed aircraft systems (UAS). This study analyzes UAS-based package delivery systems in the context of the integrated operations of crewed and uncrewed aircraft. It introduces a multi-trip, time-dependent vehicle routing problem aimed at optimizing UAS delivery routes within integrated operations. By conducting numerical simulations of helicopters (crewed aircraft) and UAS missions sharing the same airspace, the optimal UAS routes for resolving potential conflicts in the shared airspace can be effectively determined without any adverse impact on helicopter operations. Knowing the helicopter mission times in advance enables the efficient planning of UAS missions. The results of this study provide valuable insights regarding the implementation of integrated crewed and uncrewed aircraft operations.

Quadrotors are expected to play an active role in out-of-sight areas such as equipment inspection and transportation of supplies to disaster areas. However, ensuring stable and highly accurate automatic flights has become a significant challenge. Trajectory tracking control methods that combine adaptive output feedback control based on almost strictly positive real characteristics and backstepping strategy have been proposed for a quadrotor control system with nonlinearities. These methods have simple structures and are robust. However, existing adaptive control methods have the problem of singularities, owing to the use of Euler angles in the modeling of quadrotors. In this paper, we propose an adaptive control method that enables a wider range of attitude changes using quaternions. The effectiveness of the proposed method is validated through numerical simulations.

In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two-body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm.

To develop an insect-scale aerial/aquatic robot, we analyzed takeoff mechanisms to counteract surface tension, such as paddling, slapping, and clap-and-fling. Because a diving beetle, Eretes griseus, takes off directly from the water surface, a flapping-wing robot is promising as an alternative to a drone with multiple rotary wings. In this study, we first investigated diving beetle flight with a three-dimensional high-speed camera system and analyzed the motion characteristics. Subsequently, we developed a computational fluid dynamics method that tracked the water surface using a volume of fluid method, reproduced the motion with a multibody model, treated the deformation of the elastic membrane wing with the phase delay of the joint angle functions, and simulated takeoff, that is, the transition from water to air, and hovering near the water surface. The simulation result showed that during the transition, the slapping motion exerted the maximum and average lift per unit of body weight of 18 and 9.2, respectively, while those of paddling produced 0.46 and 0.23, respectively. The water surface effect improved the lift by 25% at the normalized height of less than 0.44 and disappeared at a height greater than 0.7. During hovering, while the clap-and-fling motion improved lift by 2.6% and the water surface effect was 9.8%, the synergy effect was 22%. In addition, the former enhanced it significantly after the fling, while the latter was remarkable during the wing acceleration phase. In contrast to ground effects, flapping reduced the water level and caused the ripples, dynamically changing the water surface effect.

Flying animals such as insects and birds use wing flapping for flight, occasionally pausing wing motion and transitioning into gliding to conserve energy for propulsion and achieve high flying efficiency. In this study, we have investigated the gliding performance of a gliding model based on a flapping-wing robot developed in a previous study, with the aim of developing a highly efficient flying robot that utilizes bio-inspired intermittent flight. Wind tunnel experiments with a gliding model have shown that the attitude of the wings has a strong influence on gliding performance and that a tail is effective in improving gliding performance. The results of this study provide important insights into the development of flying robots that can travel long distances with high efficiency.

There has been significant interest in the field of bio-inspired robotics, particularly in the development of flapping-wing robots from micro to bird size. Most flapping robots use lever-crank mechanisms or servomotors as wing flapping mechanisms. Servomotor-based flapping has the advantage of being able to generate various flapping patterns according to amplitude, offset, frequency, waveform, and other factors. However, it is not clear how these factors affect thrust generation. Therefore, this study focuses on the force generation and power consumption in different flapping patterns as well as the wing deformation during the flapping motion to provide some insights into the performance improvement. The results showed that the response characteristics of the actuators caused the thrust to saturate at high frequencies, and that sinusoidal pattern could generally achieve good performance and efficiency.

This paper proposes a force-sensing wing, Senswing, to enhance the intelligence of flapping-wing aerial vehicles (FWAVs). Force perception is a crucial capability for robots to interact safely and effectively in unknown environments. However, FWAVs perform flapping motions with significant acceleration and deceleration, which can cause the flexure element inside force sensors to deteriorate due to repeated loading or even fail due to impulsive forces. To address this, we constructed a force measurement system by attaching 16 strain gauges directly to the wing root while maintaining high rigidity. We confirmed that the external force measurement capability closely matched the values obtained by a six-axis force sensor, with almost no error. Additionally, when measuring aerodynamic forces during wing flapping, the sensor could detect differences in wind speed even during flapping. With this sensor, FWAVs can achieve in-flight measurement of thrust and lift through a force-sensing system.

A single-use aircraft launch system using a small helium balloon concept was proposed to elevate the likelihood of successful high-altitude flight tests above 30 km. The system, capable of carrying a payload of 0.5 kg, has been developed and reported. Completing the flight within a range of 92 km, which represents the maximum communication distance between the airborne flight system and the ground station for operational phase control, is imperative. Therefore, a straightforward method for simulating flight trajectories was outlined to determine launch windows and suitable locations to ensure flight completion within uninhabited areas. Simulation studies revealed that the shortest landing distance was obtained during summer at the selected launch site. Additionally, a parameter study was conducted to assess the influence of varying ascent velocities on the targeted flight test altitude, which depends on the payload weight and helium gas volume. Consequently, the parameter study results established the constraints for flight model design. A demonstration flight was conducted in 2023 to validate the feasibility of the system for high-altitude flight experiments. This flight successfully released the flight model at 31 km and recovered flight data before landing on the sea surface. The proposed system concept offers an expedited approach to aircraft design for operating in thin air. It enables component function tests and scaled model flights as an alternative to employing large high-altitude balloons for high-altitude experiments.

The authors have been developing small fixed-wing unmanned aerial vehicles (UAVs) for use in various scientific observations. For example, in Antarctica, atmospheric observations have been conducted using a combination of a balloon and UAV. In Ethiopia, wide-area magnetic field observations have been conducted using a UAV capable of long-range flights. These UAVs are equipped with an in-house flight control computer and are capable of automatic flights. However, although approximately 20 years have passed since the development of this computer, issues such as inadequate computing power and memory as well as insufficient number of output ports for pulse width modulation signals remain, posing challenges when constructing complicated systems. To solve these problems, we developed a flight-control computer using a 32-bit microcontroller designed to conduct atmospheric observation missions in Antarctica and withstand low temperature environments down to -40°C. Aerosol observations and sample-return missions were conducted in Antarctica, and aerosol samples were successfully collected at an altitude of 27 km using the developed computer. This paper provides detailed descriptions of the developed flight control computer named “AP-CUB-G2” and the results of the atmospheric observation flight in Antarctica.

Robotics, mechatronics, and digital technologies are advancing significantly in sports, exercise, and healthcare, and offer innovative solutions that shape the future of these fields. In Part 2 of this special issue, we examine independent research and cutting-edge developments that address new challenges and provide unique contributions to these domains.

Technological advancements in assistive devices and rehabilitation offer new solutions for improving the quality of life of individuals with physical challenges. Researchers of wearable assistive devices and prosthetics continue to devise methods to enhance mobility and support physical functions, thereby benefiting both users and healthcare providers.

Sports and motion analysis remains a key focus area, where innovative technologies are employed to analyze and improve athletic performance. By capturing and evaluating detailed movement data, these technologies can help athletes refine their techniques and achieve greater precision in their sports, thus ultimately resulting in enhanced performance and injury prevention.

As in Part 1, the studies presented in this issue demonstrate the practical applications of cutting-edge technologies and offer insights into their future potential. We hope that these contributions will inspire researchers and practitioners alike and provide a foundation for continued advancements in these exciting and impactful fields.

Workers in factories, construction sites, and farms are often exposed to the risk of physical disability and injury. Particularly, the lower back and shoulders require assistance, as injuries can make it difficult to continue working. While social concern about back injuries is high and preventive measures are taken, lesser attention is paid to shoulders, resulting in inadequate assistance and prevention mechanisms. Therefore, wearable, low-cost, and lightweight upper limb assistive devices that can be used in multiple scenarios are desired by workers. In this study, we proposed a device that uses a remote center of motion (RCM) mechanism, enabling the device to support user’s upper arm from below, and the rotational center of device to correspond with shoulder joint. The theoretical assist torque is designed to be sufficient for arm gravity compensation of Japanese males of standard body size. The calculated theoretical assist torque for each shoulder joint is about 8 Nm and maximum assist force for each arm was about 36.3 N (3.7 kgf). Experimental evaluation using a prototype of this device on three healthy adult males demonstrated a decrease in muscle activity of approximately 38% in the anterior deltoid, 31% in the middle deltoid, and 11% in the posterior deltoid as an average of all results in a dynamic experiment in which the participants performed the indicated movements.

T-cane is a primary method used to prevent falls. Although canes effectively increase stability and reduce load, the specific position of the cane tip that maximizes these effects is not yet clear. Furthermore, the cane tip position that enhances effectiveness may also increase the burden on the user. In this study, we used the center of pressure (CoP) as an indicator of stability and shoulder joint adduction torque as an indicator of burden. In this study, we propose a cane tip position that increases the stability of the cane user, but does not increase the burden, through experiment. The experiment involved healthy young male participants. The results confirmed that the CoP increased with the cane tip position. The shoulder joint adduction torque increased with the cane tip position and then remained constant. The results suggest that the participants can walk with higher stability per load when the cane tip was positioned 30 cm in front of the right foot on the ground.

Myoelectric prosthetic hands and fingers with grasping functions have challenges such as weight, cost, and grasping performance of flexible objects owing to the use of electric actuators. To resolve these problems, we propose a self-powered movable prosthetic finger using pneumatic pressure. This prosthetic finger utilizes the flexion/extension of the remaining finger of the user to drive a wire and flex or extend the finger joints. The use of a tendon (wire) and belt drives reduces the space occupied by the prosthetic finger unit compared with conventional linked prosthetic fingers. Furthermore, a sealed-air bellows is used for the joint for flexible grasping owing to passive variable-compliance and damping, which is impossible with only a tendon drive. These features have resulted in the stable grasping of various objects that are difficult to grasp using prosthetic fingers based on conventional technologies.

In sports that use tools, it is necessary to master tool manipulation with a high degree of accuracy because proficiency in tool manipulation leads to victory or defeat in a competition. The purpose of this study was to clarify the force transfer of the body, including the racket, from the perspective of vibration analysis to realize training to efficiently improve tennis skills. In this study, we measured the propagating vibration, surface electromyography of finger flexors and extensors, and racket movement under two conditions of strong- and weak-volleying in tennis and aimed to explain the meaning of the measured propagating vibration in terms of muscle control and racket kinematics. Based on the experimental results, it was confirmed that it is feasible to measure the change in stiffness from the racket to the wrist due to the muscle co-contraction owing to the propagating vibration signal intensity. These results indicate the possibility of evaluating tennis shot skill by analyzing the propagating vibrations measured using a wearable vibration measurement system.

This study aimed to determine the characteristics of the elite skiers and the techniques required to improve their performance in the men’s giant slalom alpine skiing competition by conducting a three-dimensional (3D) motion analysis. The top nine skiers were compared with the next nine skiers using 3D motion analysis in a single-gate section with an average slope of 25.6°. The results revealed the following characteristics of superior skiing techniques. (1) The skiers started the turn from a high position relative to the gate and obtained high velocity by skiing in a gentle arc using potential energy. (2) By quickly rotating and edging the skis, the skiers were able to gain centripetal force early, enter the gate, ski in the direction of the fall line, and change skiing direction timely. (3) The skiers had quick inward leaning of the body and early lowering of the pelvis on the outside ski to form an angulation posture to resist the large external forces acting on the body during the turn.

This paper presents an allocator design that considers the power consumption of rotors in the attitude and altitude control system of a hexarotor drone. Based on the power consumption model, the proposed method computes the thrust force that minimizes the total power consumption of the rotor while satisfying the control force constraints required by the controller. To obtain the rotor power consumption model, we conducted experiments on the rotor characteristics using the motors and electronic speed controllers used in the drones. Finally, numerical simulations were performed using the obtained power consumption models to compare the rotor power consumption of the proposed method with that of the conventional method, quantitatively evaluating the effectiveness of the proposed method.

This paper proposes a flexible path-planning method for conducting agricultural observation tasks using multiple autonomous guided vehicles. The observation task was formulated as the rural postman problem by graphing the agricultural field to be observed and assigning costs to mandatory and optional paths. The observation area was re-divided according to the progress of each robot’s work, and the latest path was planned to minimize the difference between the working time of individual robots, thereby reducing the overall working time. Simulations were conducted to verify the influence of the parameters used in the proposed method. The effect of workload adjustment on progress delay was verified, and the increase in overall working time owing to delay was reduced by an average of 32.9%. A performance comparison was conducted using Google OR-Tools, software specialized for combinatorial optimization. Superior solutions with shorter computation times were obtained using the proposed method.

In this paper, we present a 3-USR-type 6-degree-of-freedom (6-DOF) parallel mechanism characterized by an expansive workspace. This mechanism consists of three coupling chains, each comprising a universal pair (U), a spherical pair (S), and a rotational pair (R), in sequence from the stationary base. To achieve a large workspace, the three stationary universal pairs are designated as active pairs, with their rotational axes intersecting at a single point, thereby creating a hemispherical workspace akin to that of a serial mechanism. To implement the active universal pair within a parallel mechanism, we replaced the spherical 5-link mechanism, which originally featured two stationary active rotational pairs, with stationary active universal pairs, and conducted an inverse kinematics analysis. Subsequently, we assessed the expansive workspace of the spherical 5-link mechanism, a key factor influencing the working area of the 3-USR-type 6-DOF parallel mechanism, by examining its motion transmissibility. Based on this evaluation, we designed two compact mechanisms that provide a large workspace and allow for the configuration of all three rotational axes to intersect at a single point. We experimentally investigated the relationship between motion transmissibility and rigidity for these two types of spherical 5-link mechanisms, demonstrating that motion transmissibility can serve as an indicator of rigidity. Finally, a prototype of the 3-USR mechanism was fabricated.

Robots with parallel-link structures are generally considered useful for achieving high-speed motion; however, they are typically large in size. Robot size can be reduced by using a serial-link structure. However, their moving parts, typically having a large mass or moment of inertia, are considered unsuitable for high-speed motion. High-speed motion performance can be improved by avoiding mounting actuators on the moving parts using some method to transmit the drive force or motion. In this letter, we propose a model in which a non-pulley musculoskeletal robot, previously studied by us, is modified to avoid mounting actuators on the movable parts. We demonstrate that the robot can be controlled to achieve the target posture using this modified model. We also discuss the feasibility of high-speed motion of a prototype robot using muscular forces computed for several motion patterns based on the minimum muscle-tension change model.