Vision aided dynamic exploration on bipedal robots poses an integrated challenge for perception and control. Rapid walking motions as well as the vibrations caused by the landing-foot contact-force introduce critical uncertainty in the visual-inertial system, which can cause the robot to misplace its feet placing on complex terrains and even fall over. In this paper, we present a streamlined integration of an efficient geometric footstep planner and the corresponding walking controller for a humanoid robot to dynamically walk across rough terrain at speeds up to 0.3 m/s. To handle perception uncertainty that arises during dynamic locomotion, we present a geometric safety scoring method in our footstep planner to optimally select feasible path candidates. In addition, the real-time performance of the perception pipeline allows for reactive locomotion such as generating a new corresponding swing leg trajectory in mid-gait if a sudden change in the terrain is detected. The proposed perception-control pipeline is evaluated and demonstrated with real experiments using a full-scale humanoid to traverse across various terrains.

This paper proposes a novel algorithm for joint space position/torque hybrid control of a mammal-type quadruped robot. With this control algorithm, the robot demonstrated both dynamic locomotion and push reaction abilities without the need for torque control in the ab/ad joints. Based on the tipping and slipping condition of the legged robot, we showed that reaction to a typical push in the horizontal direction does not require full contact-force-control in the frontal plane. Furthermore, we showed that position/torque hybrid control in Cartesian space is directly applicable to joint space hybrid control due to the joint configuration of the quadruped robot. We conducted experiments on our legged robot platform to verify the performance of our hybrid control algorithm. With this approach, the robot displayed stability while walking and reacting to external push disturbances.

This study proposes a biped-robot pelvis-kinematics estimator based on the touch-point updating method. Because the pelvis frame is used as the base coordinate for the control, the kinematics of it with respect to the global frame should be precisely estimated. To this end, it was necessary to know where the robot made contact with the ground. The touch-point concept was introduced as the temporal contact-point, which was instantly the robot's rotation center. By updating this point, the biped's global pelvis-kinematics could be estimated. The proposed estimator was implemented into the actual robot, and its superiority was verified through ground-truth data.

This paper introduces an obstacle-avoiding algorithm for bipedal robots, especially in push recovery situations. Typically, There are many algorithms that plan footstep to avoid obstacles based on vision recognition data. However, if the robot is pushed, the planned footprint will change, and thus, there is no guarantee that it will avoid obstacles. Although modified stepping positions can be limited, the robot's stability is not assured. Our proposed algorithm focuses on avoiding obstacles through vision recognition in push recovery situations and generating compensation actions for instability by restricting modified footsteps. We fuse vision feedback with our previous push recovery algorithm, which optimizes the ankle, hip, and stepping strategies. We build simple grid data using vision recognition and apply it to the inequality constraint of the stepping position. We validate the effectiveness of our algorithm using the bipedal platform GAZELLE with the Kinect V2 RGBD sensor.

As the aging population grows at a rapid rate, there is an ever growing need for service robot platforms that can provide daily assistance at practical speed with reliable performance. In order to assist with daily tasks such as fetching a beverage, a service robot must be able to perceive its environment and generate corresponding motion trajectories. This becomes a challenging and computationally complex problem when the environment is unknown and thus the path planner must sample numerous trajectories that often are sub-optimal, extending the execution time. To address this issue, we propose a unique strategy of integrating a 3D object detection pipeline with a kinematically optimal manipulation planner to significantly increase speed performance at run-time. In addition, we develop a new robotic butler system for a wheeled humanoid that is capable of fetching requested objects at 24% of the speed a human needs to fulfill the same task. The proposed system was evaluated and demonstrated in a real-world environment setup as well as in public exhibition.

In this paper, we propose a biped walking controller that optimized three push recovery strategies: the ankle, hip, and stepping strategies. We suggested formulations that related the effects of each strategy to the stability of walking based on the linear inverted pendulum with flywheel model. With these relations, we could set up an optimization problem that integrates all the strategies, including step time change. These strategies are not applied hierarchically, but applied according to each weighting factor. Various combinations of weighting factors can be used to determine how the robot should respond to an external push. The optimization problem derived here includes many nonlinear components, but it has been linearized though some assumptions and it can be applied to a robot in real time. Our method is designed to be robust to modeling errors or weak perturbations, by exploiting the advantages of the foot. Hence, it is very practical to apply this algorithm to a real robot. The effectiveness of the walking controller has been verified through abstracted model simulation, full dynamics simulation, and a practical robot experiments.

This work proposes a humanoid robot center of mass (COM) estimation framework based on the compliant inverted pendulum model and the robust estimator. Humanoids' limited structural stiffness and relatively long legs result in undesired flexibility, and this undesired motion hinders the state estimation. The models used in previous studies were either not suitable for estimation or too simple to express these key characteristics of humanoid robots. Here, to enhance the estimation performance, the compliant inverted pendulum model, which is developed by attaching a spring and damper to the original pendulum, is adopted. The additional elements can represent the mechanical deformation and undesired flexibility. This model can reflect the important characteristics of the humanoid robot while taking advantage of the merits of the sing-mass model. In addition, a robust state estimator that was proposed in our previous work is adopted to compensate for an estimation error caused by a modeling error. Using these two factors, an improved COM kinematics estimates could be obtained.

Most state-of-the-art torque control-based legged robots show excellent performance, exceeding that of conventional position control-based robots. Many conventional position control-based legged robots have high gear ratios, but do not have joint torque sensors. In addition, some robots cannot generate current for controlling the motor torque. To apply torque control-based walking algorithms to a position control-based humanoid robot, we proposed current control using a motor thermal model and realized joint torque control by compensating for the joint dynamics and robot dynamics. We conducted experiments to verify the performance of the Hubo2 platform developed in 2008 by applying a full-body dynamics control framework. The results confirmed the possibility of using torque control algorithms with existing position-based robots.

This paper describes a humanoid robotics platform (DRC-HUBO+) developed for the Defense Advanced Research Projects Agency Robotics Challenge (DRC) Finals. This paper also describes the design criteria, hardware, software framework, and experimental testing of the DRC-HUBO+ platform. The purpose of DRC-HUBO+ is to perform tasks by teleoperation in hazardous environments that are unsafe for humans, such as disaster zones. We identified specific design concepts for DRC-HUBO+ to achieve this goal. For a robot to be capable of performing human tasks, a human-like shape and size, autonomy, mobility, manipulability, and power are required, among other features. Furthermore, modularized joints and a user-friendly software framework were emphasized as design concepts to facilitate research on the robot tasks. The DRC-HUBO+ platform is based on DRC-HUBO-1 and HUBO-2. The torque of each joint is increased compared to that in DRC-HUBO-1 owing to its high reduction ratio and air-cooling system. DRC-HUBO+ is designed with an exoskeletal structure to provide it with sufficient stiffness relative to its mass. All wires are enclosed within the robot body using a hollow shaft and covers to protect the wires from external shock. Regarding the vision system, active cognition of the environment can be realized using a light-detection and ranging sensor and vision cameras on the head. To achieve stable mobility, the robot can transition from the bipedal walking mode to the wheel mode using wheels located on both knees. DRC-HUBO+ has 32 degrees of freedom (DOFs), including seven DOFs for each arm and six DOFs for each leg, and a solid and light body with a height of 170 cm and a mass of 80 kg. A software framework referred to as PODO, with a Linux kernel and the Xenomai patch, is used in DRC-HUBO+.

The unified approach algorithm to control a mobile robot is useful in simplifying path planning and inverse kinematics by considering a mobile platform as hypothetical joints. Applying the damped least square method by using the Jacobian prevents the divergence of the joint angle. However, it is possible to violate the nonholonomic constraint on mobility by distorting the Jacobian. In robot manipulation, the end-effector position error due to a violation of the constraint can be fatal, because such an error can damage a nearby object or the robot itself. In this paper, we propose a method that strictly guarantees nonholonomic constraints on a mobile manipulator. We also propose a compensation technique for faster convergence of the position and orientation of the end effector. The effectiveness of the proposed methods was confirmed through simulations.

In this paper we introduce a biped foot placement controller based on capture point (CP) feedback control. This capture point feedback controller generates desired Zero Moment Point (ZMP) according to current capture point error. We call this desired ZMP as Control-ZMP (cZMP). Using this cZMP, we constructed (i) a disturbance adapting walking pattern generator, (ii) an ankle torque reference generator, (iii) a landing foot position adjustor and, (iv) a step time adjustor. By applying these controllers, the biped system becomes robust over uneven terrain and external pushing disturbances. We considered cZMP as a key indicator of bipedal walking stability. If the cZMP is within the support polygon, the robot will track the cZMP by using (i) and (ii). If the cZMP is outside of the support polygon, the robot will change footstep position and time by using (iii) and (iv) (COM pattern will be changed by (i) too). Capture point dynamics is described based on a linear inverted pendulum (LIP) model. The performance of the suggested control algorithm is validated in the Choreonoid simulator with a model of DRC-HUBO+ [11], [12].

In this paper, a current control scheme for the brushless DC (BLDC) motor is proposed. In order to estimate the phase current, it employs the adaptive extended Kalman filter (EKF) and measurement of a single DC link current. When estimating the motor phase current, measurement of a single DC link current is scaled by PWM (Pulse Width Modulation) duty. If the PWM duty is very small, the sensitivity of the measurement noise is dramatically increased. In order to solve this problem adaptive EKF is applied. Therefore, estimated phase current using adaptive EKF prevents the possible occurrence of an unstable situation due to the sensitivity. The accuracy of the proposed current control scheme was confirmed by comparing the estimated current by adaptive EKF and the measured actual phase current. In additions, the effectiveness was verified through the current-control time response of the when the PWM duty for the control was close to zero. By using the proposed current control scheme, robust current control of the BLDC motor was possible with a single DC link current.

This paper presents a vision system and a depth processing algorithm for DRC-HUBO+, the winner of the DRC finals 2015. Our system is designed to reliably capture 3D information of a scene and objects and to be robust to challenging environment conditions. We also propose a depth-map upsampling method that produces an outliers-free depth map by explicitly handling depth outliers. Our system is suitable for robotic applications in which a robot interacts with the real-world, requiring accurate object detection and pose estimation. We evaluate our depth processing algorithm in comparison with state-of-the-art algorithms on several synthetic and real-world datasets.

For robots, a flexible approach is very important. Even when the robot is a humanoid, it does not have to perfectly mimic human motion. If necessary, the humanoid robot can adapt to other technologies even when these technologies make it different from humans. In a real environment or a disaster environment, humanoid robots are a good solution to assist humans. However, the stability problem of biped locomotion remains. In this paper, we introduce a new strategy of attaching a wheel to our humanoid robot in order to achieve mobility efficiency with a bipedal walking and wheel driven mode. Additionally, this strategy can enhance the stability. Through the proposed method, the humanoid robot can traverse uneven terrain and climb stairs with a walking motion, and can move safely with wheels on the ground. In addition, a method will be presented that can enhance the performance of wheel movement by using redundant joints and sensors on the humanoid robot. Various experiments and the DARPA Robotics Challenge results validate the efficiency and the feasibility of the proposed strategy.

For a biped robot to keep walking, basic walking patterns are needed. One method to generate these patterns is to use an extrapolated center of mass (XcoM) concept and constant zero-moment point (ZMP) patterns. However, center of mass (CoM) patterns generated from such a method have discontinuous ZMP and CoM accelerations. For solving this problem, we propose a method in which continuous ZMP patterns can be simply generated from constant ones. In addition, experimental results of forward walking are presented. The results demonstrate that this pattern generation method can give a starting point for walking robots.

We present an object proposal method which utilizes the 3D data obtained from a depth sensor as well as the color information of images. Our object proposal method is designed to improve the performance of the object detection for a mobile robot equipped with a camera and a laser scanner. Compared to traditional object proposal methods using only 2D images, the proposed method provides much less number of candidate windows for object detection. We show less than 100 object proposal windows per image using the proposed method result in high recall tested on the public dataset. Our method presents object proposals in 3D space as well as in 2D image thus it can further be applied to following tasks for mobile robots such as 3D location and pose estimation of the target object after successful object detection. We validate our method using the real-world object detection dataset for outdoor mobile robots captured during the DRC Finals 2015 and the public dataset for comparison with the previous methods.

This paper presents an autonomous planning and control framework for humanoid robots to climb general ladder- and stair-like structures. The approach consists of two major components: 1) a multi-limbed locomotion planner that takes as input a ladder model and automatically generates a whole-body climbing trajectory that satisfies contact, collision, and torque limit constraints; 2) a compliance controller which allows the robot to tolerate errors from sensing, calibration, and execution. Simulations demonstrate that the robot is capable of climbing a wide range of ladders and tolerating disturbances and errors. Physical experiments demonstrate the DRC-Hubo humanoid robot successfully mounting, climbing, and dismounting an industrial ladder similar to the one intended to be used in the DARPA Robotics Challenge Trials.

This video presents our preliminary work towards addressing the ladder climbing event in DARPA Robotics Challenge (DRC) using DRC-Hubo robot. A ladder-climbing motion planner is developed which generates a collision-free, stable quasi-static trajectory for execution. Compliance control is enabled on arm joints to compensate for the calibration error, modeling error and control error. We have demonstrated that DRC-Hubo can robustly climb a variety of ladders in simulation and successfully climb a ship ladder on the hardware.

This paper introduces a motion planning method for a rapid mobile manipulator using an inverted pendulum model. We design a linear quadratic optimal controller to stabilize ZMP. The two kinds of ZMP stabilization strategies (Fixed ZMP and Relaxed ZMP) are proposed. The highly geared manipulator is controlled by a Cartesian computed torque (CCT) control for compliant motion. A rapid mobile manipulator called KDMR-1 has been developed for its application. The high acceleration and speed performances of the proposed methods are shown by a rapid maneuvering experiment.

This work shows a method of creating trajectories to achieve end-effector velocity control for high degree of freedom position controlled, high-gain, robots. The focus of this work is throwing an object. It is shown that the full reachable area of the end-effector does not need to be known to achieve the desired velocity when a good collision model of the robot is available. The end-effector velocity (magnitude and direction) is specified as well as a duration of this velocity. A sparse map of reachable end-effector positions in free space and the corresponding poses in joint space is created using random sampling in joint space and forward kinematics. The desired trajectory in free space is placed within the sparse map with the first point of the trajectory being a known pose from the original sparse map. The Jacobian Transpose Controller method of inverse kinematics is then used to find the subsequent points in the trajectory. Each pose in the trajectory is checked against the collision model to guarantee no self-collisions. This method was tested on the 130 cm tall full size humanoid Jaemi Hubo and its virtual representation.

In this paper, we developed a novel dynamic mobile platform capable of transforming between four wheel rapid driving mode with ZMP stabilization and two wheel balancing mode. Usually, the four wheel mobile platforms have low acceleration due to the high center of mass. Using the feed-forward ZMP stabilization method, we achieved high acceleration performance with maintaining stable ZMP. We use a LQR controller for two wheel balancing mode. In the two wheel balancing mode, there are two different driving modes, self-balancing mode, human-riding mode. The transformation between four wheel and two wheel mode is made possible by swing up and swing down control method. We prove the dynamic performance of mobile platform by experimental results.

This paper discusses balancing for a hopping humanoid biped against various disturbances. Contrary to other studies, the present work focuses on the practical experiment with a real humanoid biped, HUBO2. Also, hopping is focused on among various types of locomotion since hopping is simple movement but more dynamic rather than walking. Two control strategies are proposed according to the magnitude of the disturbances. The one is the posture balance control for small disturbance, which uses the ankle torque of the stance leg. The other is to use the posture balancing control and the landing position control together for large disturbance. The landing position controller changes the landing position of the swing foot to maintain stability. The closed form solution of the landing position controller is addressed with the simplified model. As this simplification, both controllers are used together since the landing position controller cannot maintain a perfect balance alone. To this end, practical experiments with HUBO2 are conducted. In the experiments, HUBO2 maintains a balance against not only small disturbance but also large disturbance such as pushing through the proposed control strategies.

This paper introduces a novel approach to control a wheeled inverted pendulum when a disturbance is applied by a human. The interaction between a human and a wheeled inverted pendulum involves a pulling or pushing force. This type of action is a severe disturbance for a wheeled inverted pendulum, as the wheeled inverted pendulum tends to maintain its initial position if there is no desired input. Thus, there are many possibilities for the wheeled inverted pendulum to be unstable as a result of interactions with humans. To solve this problem, the control algorithm of a wheeled inverted pendulum was designed to move in coordination with the external force of a human. This control algorithm is termed human-friendly motion control. It contains an optimal controller using a full-state feedback and a reduce-order disturbance observer. The disturbance torque from a human was estimated, and the estimated disturbance torque was used to generate a position reference for the human-friendly motion. This control algorithm keeps the wheeled inverted pendulum stable even when a severe disturbance is applied.

In the walking control of a biped humanoid robot, the walking performance is seriously affected by the initial home posture. An important thing is that the initial home posture of real robot is slightly different at every setting because a zero position of joint is not exactly the same. Accurate and consistent initial home posture is essential when we compare and analyze walking control algorithms. In general, the conventional method for electric motor uses an incremental encoder with a limit switch or an absolute encoder such as potentiometer to make a zero position. However, this method for the multi-axis humanoid robot is difficult, time-consuming, and inaccurate. Furthermore, it has the disadvantage that additional limit switch or absolute encoder can interfere with the design objective of compactness. This paper describes a novel adjustment method of home posture for a humanoid robot utilizing incremental encoders, an inertial sensor and force torque sensors. Four kinds of controllers are proposed and adjusted offsets are measured when outputs of the controllers are converged. The experimental results from KHR-2 show the effectiveness of the proposed algorithm.

This paper describes an algorithm about online gait trajectory generation method, controller for walking, brief introduction of humanoid robot platform KHR-3 (KAIST Humanoid Robot-3: HUBO) and experimental result. The gait trajectory has continuity, smoothness in varying walking period and stride, and it has simple mathematical form which can be implemented easily. It is tested on the robot with some control algorithms. The gait trajectory algorithm is composed of two kinds of function trajectory. The first one is cycloid function, which is used for ankle position in Cartesian coordinate space. Because this profile is made by superposition of linear and sinusoidal function, it has a property of slow start, fast moving, and slow stop. This characteristics can reduce the over burden at instantaneous high speed motion of the actuator. The second one is 3rdorder polynomial function. It is continuous in the defined time interval, easy to use when the boundary condition is well defined, and has standard values of coefficients when the time scale is normalized. Position and velocity values are used for its boundary condition. Controllers mainly use F/T(Force/Torque) sensor at the ankle of the robot as a sensor data, and modify the input position profiles (in joint angle space and Cartesian coordinate space). They are to reduce unexpected external forces such as landing shock, and vibration induced by compliances of the sensors and reduction gears, because they can affect seriously on the walking stability. This trajectory and control algorithm is now on the implementing stage for the free-walking realization of KHR-3. As a first stage of realization, we realized the marking time and forward walking algorithm with variable frequency and stride

To celebrate the 100th anniversary of the announcement of the special relativity theory of Albert Einstein, KAIST HUBO team and hanson robotics team developed android type humanoid robot Albert HUBO which may be the world's first expressive human face on a walking biped robot. The Albert HUBO adopts the techniques of the HUBO design for Albert HUBO body and the techniques of hanson robotics for Albert HUBO's head. Its height and weight are 137cm and 57Kg. Albert HUBO has 66 DOFs(31 for head motions and 35 for body motions) And head part uses 'Fubber' materials for smooth artificial skin and 28 servo motors for face movements and 3 servo motors for neck movements are used for generating a full range of facial expressions such as laugh, sadness, angry, surprised, etc. and body is modified with HUBO(KHR-3) introduced in 2004 to join with Albert HUBO's head and 35 DC motors are embedded for imitating various human-like body motions.

In this paper, we describe the mechanical design, system integration and dynamic walking of the humanoid, KHR-2 (KAIST Humanoid Robot– 2). KHR-2 has 41 DOFs in total, that allows it to imitate various human-like motions. To control all joint axes effectively, the distributed control architecture is used, which reduces computation burden on the main controller, and allows convenient system. A servo motor controller was used as the sub-controller, whereas a 3-axis force/torque sensor and an inertia sensor were used in the sensory system. The main controller attached on the back of KHR-2 communicates with the sub-controllers in real-time through CAN (Controller Area Network) protocol. Windows XP was used as the operation system, whereas RTX HAL extension commercial software was used to realize the real-time control capability in Windows environment. We define the walking pattern and describe several online controllers in each stage. Some of the experimental results of KHR-2 are also presented.

This work presents three online controllers for maintaining dynamic stability of a humanoid robot using force/torque sensor. Those are damping controller, landing orientation controller and landing position controller. The legs of a humanoid robot are relatively long and serially connected with compliant force/torque sensor at the ankle. This architecture has the inherent characteristics of a lightly damped system. Most research on balance control overlook the deterministic vibration caused by structural compliance. In addition, the vibration was not positively considered to improve the characteristics of the system. Therefore, a simple inverted pendulum model with compliant joint is proposed. For this model, the damping controller that increases system damping is proposed as a balance controller. Furthermore, the performance of maintaining balance against external forces is experimentally shown. A landing orientation controller at the ankle joints is presented to manage fast and stable ground contact. A landing position controller is implemented in order to modify the prescribed trajectory of the swing foot and to reduce the landing impact during unexpected landing. The effectiveness of the proposed controllers is confirmed by walking experiments that has been applied on the KAIST humanoid robot platform KHR-1.

Since conventional above-knee prostheses are passive type devices with constant mechanical properties, the knee joint motions are not similar to that of normal persons. On the other hand, active type prostheses can improve the swing phase gait but these are expensive, heavy and consume large energy. Thus we propose a semi-active prosthesis using the rotary magnetorheological (MR) damper. The torque dissipation in the knee joint can be controlled by the magnetic field induced by the solenoid. A 3-DOF leg simulator has been developed to generate various hip motions and analyze the results of walking motions. The tracking control of knee joint angle was performed with this leg simulator. The experiment shows that the proposed prosthesis system has good performance in swing phase. We applied the repetitive controller in conjunction with the computed control law and PD control law. This algorithm reduces the RMS tracking error as the repetitions of the tracking. Moreover, the proposed prosthesis system is adaptable to walking speed.

In this paper, the new type biped walking robot which is composed of a minimum number of links just for walking and its appropriate gaits are experimented. The proposed new gaits for this robot are: the four-crossing, crawling, standing and turning gaits. Dynamically stable walking of the biped robot is implemented by satisfying the stability condition of the zero moment point.

Trailer systems consist of a steering tractor and a passive trailer linked together with rigid free joint. The backward driving of a trailer system is more difficult than the forward driving, because the backward driving of the trailer system is unstable. We study the backward tracking control for trailer systems and implement the asymptotically stable tracking controller using the Lyapunov direct method. We perform some experiments using a visual feedback system. The experimental results show stable responses and the effectiveness of our method.

A soccer robot system has many characteristic factors of a multi-agent system. We have built a soccer robot system to participate in MIROSOT96. In this paper, we present some factors to be considered in building the system. Since how to constitute the system is very important, we have surveyed architectures of multi-agent systems. Considering the nature of the soccer robot game, we select a centralized online system for the soccer robot system. We give the reasons of selection. Our system is composed of several parts-a robot, a supervisor, vision system, communication devices. In this paper, the detailed descriptions of each component of our system are provided for later development. Our system is intended to play a soccer game, but, it can be used in other area such as solving the optimization problem of the path planning of multiple mobile robots with distributed obstacles and acquiring purposive behaviors of robots by vision-based learning.

There are some learning problems for which a priori information, such as the Jacobian of mapping, is available in addition to input-output examples. This kind of information can be beneficial in neural network learning if it can be embedded into the network. This article is concerned with the method for learning the mapping and available Jacobian simultaneously. The basic idea is to minimize the cost function, which is composed of the mapping error and the Jacobian error. Prior to developing the Jacobian learning rule, we develop an explicit and general method for computing the Jacobian of the neural network using the parameters computed in error backpropagation. Then the Jacobian learning rule is derived. The method is simpler and more general than tangent propagation (Simard, Victorri, Le Cun, & Denker, 1992). Through hybridization of the error backpropagation and the Jacobian learning, the hybrid learning algorithm is presented. The method shows good performance in accelerating the learning speed and improving generalization. And through computer experiments, it is shown that using the Jacobian synthesized from noise-corrupted data can accelerate learning speed.

Though the mobility of a walking robot is superior to a wheel type robot in hazardous terrain, it is not easy for a walking robot to walk avoiding arbitrarily arrayed forbidden areas in the terrain. In order not to step on the forbidden areas, the gait of a walking robot should be aperiodic. But it is very complicated to analyze aperiodic gaits. In this paper, the authors focus on aperiodic gaits for straight motion and spinning motion. Based on the study of optimal periodic gaits, the authors show the support condition that enables aperiodic motion with preservation of the leg-lifting sequence of optimal periodic gaits. The authors introduce a schematic design of a leg mechanism that is spatially decoupled by using a 2-dimensional pantograph mechanism and a vertical linear actuator.

This paper adopts an incremental unit computation method to obtain the inverse kinematics of a three-axis articulated robot. This method starts by defining incremental units in joint and Cartesian spaces, which represent the position resolutions in each space. With this approach the calculation of the inverse Jacobian matrix can be realized through a simple combinational logic gate. Furthermore, the incremental direct kinematics can be solved by using a digital differential analyzer integrator. The hardware architecture to implement the algorithm is also described. Through applying the hardware realized by an erasable programmable logic device to the straight-line trajectory of an experimental robot, the end effector's maximum speed of 12.6 m/s has been obtained.