One-legged Robot Research Articles

A compliant leg design combining pantograph structure with leaf springs

AbstractWe proposed a compliant leg configuration that enhances the conventional pantograph design with leaf springs. The following facts characterize the proposed configuration: (1) Due to the use of the pantograph structure, the mass is centralized around the hip joint, reducing the lower leg inertia; (2) Leaf springs are chosen as elastic parts to increase energy efficiency and estimate foot-end contact forces. Compared with coil springs, leaf springs require no guide rails to deploy, and their stiffness can be easily adjusted through shape cutting. Analytical models are introduced to analyze the leg’s stiffness and estimate the contact forces only with the deflections of leaf springs. A one-leg robot based on the proposed design is built, and various experiments are conducted. Experiments regarding the stiffness calibration and the contact forces estimation showed an acceptable agreement with the analytical model. Experiments of dropping demonstrate the feasibility of the leg to perform spring-like behaviors. Experiments of periodic hopping demonstrate the feasibility of using spring deflections to detect touch-down events. For energy efficiency, it is also observed that the elastic leg has a 20% increment concerning the jumping height in the flight phase, compared with the one where leaf springs are replaced with rigid materials.

The time-freezing reformulation for numerical optimal control of complementarity Lagrangian systems with state jumps

This paper introduces a novel time-freezing reformulation and numerical methods for optimal control of complementarity Lagrangian systems (CLS) with state jumps. We cover the difficult case when the system evolves on the boundary of the dynamic’s feasible set after the state jump. In nonsmooth mechanics, this corresponds to inelastic impacts. The main idea of the time-freezing reformulation is to introduce a clock state and an auxiliary dynamical system whose trajectory endpoints satisfy the state jump law. When the auxiliary system is active, the clock state is not evolving, hence by taking only the parts of the trajectory when the clock state was active, we can recover the original solution. The resulting time-freezing system is a Filippov system that has jump discontinuities only in the first time derivative instead of the trajectory itself. This enables one to use the recently proposed Finite Elements with Switch Detection (Nurkanović et al., 2022), which makes high accuracy numerical optimal control of CLS with impacts and friction possible. We detail how to recover the solution of the original system and show how to select appropriate auxiliary dynamics. The theoretical findings are illustrated on a nontrivial numerical optimal control example of a hopping one-legged robot.

Controlling a One-Legged Robot to Clear Obstacles by Combining the SLIP Model with Air Trajectory Planning

Legged animals can adapt to complex terrains because they can step or jump over obstacles. Their application of foot force is determined according to the estimation of the height of an obstacle; then, the trajectory of the legs is controlled to clear the obstacle. In this paper, we designed a three-DoF one-legged robot. A spring-loaded inverted pendulum model was employed to control the jumping. Herein, the jumping height was mapped to the foot force by mimicking the jumping control mechanisms of animals. The foot trajectory in the air was planned using the Bézier curve. Finally, the experiments of the one-legged robot jumping over multiple obstacles of different heights were implemented in the PyBullet simulation environment. The simulation results demonstrate the effectiveness of the method proposed in this paper.

Stable and Fast Planar Jumping Control Design for a Compliant One-Legged Robot.

Compliant bipedal robots demonstrate a potential for impact resistance and high energy efficiency through the introduction of compliant elements. However, it also adds to the difficulty of stable control of the robot. To motivate the control strategies of compliant bipedal robots, this work presents an improved control strategy for the stable and fast planar jumping of a compliant one-legged robot designed by the authors, which utilizes the concept of the virtual pendulum. The robot was modeled as an extended spring-loaded inverted pendulum (SLIP) model with non-negligible torso inertia, leg inertia, and leg damping. To enable the robot to jump forward stably, a foot placement method was adopted, where due to the asymmetric feature of the extended SLIP model, a variable time coefficient and an integral term with respect to the forward speed tracking error were introduced to the method to accurately track a given forward speed. An energy-based leg rest length regulation method was used to compensate for the energy dissipation due to leg damping, where an integral term, regarding jumping height tracking error, was introduced to accurately track a given jumping height. Numerical simulations were conducted to validate the effectiveness of the proposed control strategy. Results show that stable and fast jumping of compliant one-legged robots could be achieved, and the desired forward speed and jumping height could also be accurately tracked. In addition to that, using the proposed control strategy, the robust jumping performance of the robot could be observed in the presence of disturbances from state variables or uneven terrain.

Pre-Landing Control for a Legged Robot Based on Tiptoe Proximity Sensor Feedback

The moment a legged robot touches the ground, the tip of its toe can experience a significant impact force. It is preferable to keep the landing impact force small because it causes imbalance and damage to the frame, motors, gears, and other components of the robot legs. In this paper, we propose a control method to mitigate the landing impact force by preliminary motion based on the proximity information of the tiptoe before landing. A proximity sensor is mounted on the tiptoe to detect the ground before landing, and feedback control is applied according to the sensor output to reduce the impact force. In landing experiments using a one-legged robot equipped with a proximity sensor on a tiptoe, we evaluated the effects of changing the sensor offset distance and the feedback gains on impact force mitigation. The results show that the landing impact force was mitigated by reducing the relative velocity of the tiptoe and the ground using the proposed proximity feedback control.

Dynamics Simulation of a One-legged Robot with a Flexible Joint for Generating Landing Impact Absorbing Motion

Dynamics Simulation of a One-legged Robot with a Flexible Joint for Generating Landing Impact Absorbing Motion

Design, Optimization and Evaluation of a New Cylinder Attachment Geometry to Improve the Hopping Height of the Bionic One-Legged Robot

Due to the high power-to-weight ratio and robustness, hydraulic cylinders are widely used in the actuation area of the legged robot systems. Most of these applications are focused on the motion stability, gait planning, and impedance control. However, the energy efficiency of the legged robotic system is also a very important point to be considered. Hopping locomotion requires a fast extension of the tibia leg at the end of the take-off phase, which causes a continuous increment of the cylinder velocity under the normally direct attachment geometry (DAG) of the cylinder. This leads to a high flow requirement, large pressure drop, and low energy efficiency. Therefore, we propose a four-bar mechanism attachment geometry (FMAG) to improve the energy efficiency by refining the relationship between the joint angle and cylinder displacement trend. The kinematic and dynamic models of the bionic one-legged robot are built to calculate the hopping process during the take-off phase. Based on the established dynamic models, the design parameters in both the DAG and FMAG are optimized to maximize the hopping height, respectively. The hopping experiments are conducted to verify the effectiveness of the new attachment geometry. The experimental results show that the robot hopping energy at the end of the take-off phase increases 14.8% under the FMAG.

Simulation of Upward Jump Control for One-Legged Robot Based on QP Optimization.

An optimization framework for upward jumping motion based on quadratic programming (QP) is proposed in this paper, which can simultaneously consider constraints such as the zero moment point (ZMP), limitation of angular accelerations, and anti-slippage. Our approach comprises two parts: the trajectory generation and real-time control. In the trajectory generation for the launch phase, we discretize the continuous trajectories and assume that the accelerations between the two sampling intervals are constant and transcribe the problem into a nonlinear optimization problem. In the real-time control of the stance phase, the over-constrained control objectives such as the tracking of the center of moment (CoM), angle, and angular momentum, and constraints such as the anti-slippage, ZMP, and limitation of joint acceleration are unified within a framework based on QP optimization. Input angles of the actuated joints are thus obtained through a simple iteration. The simulation result reveals that a successful upward jump to a height of 16.4 cm was achieved, which confirms that the controller fully satisfies all constraints and achieves the control objectives.

Posture Stabilization Control of a One-Legged Hopping Robot Based on Periodic Discrete-Time System

Posture Stabilization Control of a One-Legged Hopping Robot Based on Periodic Discrete-Time System

Falling Motion for Drop Impact Absorbing by a One-Legged Robot With Soft Outer Shells and Joint

Falling Motion for Drop Impact Absorbing by a One-Legged Robot With Soft Outer Shells and Joint

Dynamic stability and control of a novel handspringing robot

In the field of mobile robotics, legged locomotion plays an essential role in transporting robots over various terrain types. A significant portion of research on legged robots has been focused on one-legged robots. In contrast with different types of locomotion of multi-legged robots, one-legged robots have only one type of motion, called hopping. Hopping motion, as a type of hybrid behavior, is generally comprised of flight and stance phases. Dynamic stabilizing of hopping motion provides a challenging control problem because of its nonlinear and hybrid behavior. The majority of one-legged hopping robots investigated so far are only capable of hopping with one side of their leg. In this paper, a one-legged handspringing robot is proposed as a novel one-legged hopping robot able to hop with both its springy sides. In handspringing motion, the robot is able to clear obstacles with greater height compared to the well-known hopping motion with the same initial condition. The proposed robot has only one rotary actuator and the slipping phase in the robot's real motion is considered in its modeling. PD controllers are applied to provide different stable limit cycles to control the robot's forward velocity.

Vertical Jumping Motion of One-Legged Jumping Robot with Pneumatic Actuators

Vertical Jumping Motion of One-Legged Jumping Robot with Pneumatic Actuators

Numerical method for attitude motion planning of one-legged hopping robot

Numerical method for attitude motion planning of one-legged hopping robot

A flight-phase terrain following control strategy for stable and robust hopping of a one-legged robot under large terrain variations

This work demonstrates a simple, once per step, flight-control method for robots running on a planar unknown rough-terrain environment. The robot used to exemplify these control strategies is the ParkourBot, a spring loaded inverted pendulum (SLIP)-based robot. The SLIP model is widely used for the description of humans and animals running motion and has been the basis for many robots. A known control scheme for increasing robustness of the conservative, SLIP model is the swing leg retraction (SLR) method. Despite of the SLR’s popularity, it is not intended to be used on the more realistic, non-conservative damped SLIP model. On the damped SLIP model, the SLR controller failed to provide adequate results, therefore, we have derived a new simple, flight-phase control method called polynomial energy insertion (PEI). The new PEI method is based on the dead-beat solution of the damped simplified instantaneous SLIP (iSLIP) model, which assumes an infinitely stiff spring. Unlike the SLR which, starting from apex, changes the leg angle monotonically during flight, the PEI requires the leg length (hence, energy insertion) to change monotonically throughout the flight phase. Interestingly, the leg angle remains nearly constant. In simulations and experiments, we have compared the newly developed PEI to the previous SLR method. We have found that since the SLR does not control the horizontal velocity, it looses its stability under rough terrain. The PEI method was able to control the horizontal velocity and height from ground and hence showed great improvement in robustness to rough terrain. Moreover, in both simulations and experiments the PEI methods showed an increase in the mean jumps to failure of more than 30% compared to SLR-based controllers.

局所的PID制御器を用いた1脚ロボットの姿勢制御

Although legged robots have been researched for more than 20 years, their movement is not quick as same as animals. Abilities of a leg are not clarified. The objective of this research is to clarify the abilities and functions by manufacturing a one-legged robot. The one-legged robot is designed as almost same as human legs. Since it has not only electric motors but air cylinders in its thigh and calf as actuators, it has enough power to move. Local PID controllers for body attitude and center of gravity work to stabilization of standing control for the one-legged robot.

一脚ジャンピングロボットの跳躍パターンに関する研究

一脚ジャンピングロボットの跳躍パターンに関する研究

Coordinated Motion Control between the Knee and Ankle Joints for One-legged Robot Based on Particle Swarm Optimization Algorithm

Coordinated Motion Control between the Knee and Ankle Joints for One-legged Robot Based on Particle Swarm Optimization Algorithm

Evaluation of Effect of Cushioning Material and Servo Gain on Parachute Landing Impact Using a Small One-Legged Robot

Evaluation of Effect of Cushioning Material and Servo Gain on Parachute Landing Impact Using a Small One-Legged Robot

Posture control of one-legged robot based on periodic discrete time system

Posture control of one-legged robot based on periodic discrete time system

電磁クラッチを用いた1脚ロボットの連続跳躍

電磁クラッチを用いた1脚ロボットの連続跳躍