Real-time Walking Pattern Generation Research Articles

Analytical solution to a time-varying LIP model for quadrupedal walking on a vertically oscillating surface

This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s2) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters.

Humanoid walking pattern generation based on model predictive control approximated with basis functions

ABSTRACTThis paper proposes a real-time walking pattern generator (WPG) based on model predictive control (MPC). Since reducing the calculation time is a crucial problem in real-time WPG, we consider introducing basis functions to reduce the number of control input. The control inputs in the MPC are described by a series of basis functions. Compared with the standard discrete-time MPC formulation, the approach with basis functions requires fewer optimization variables at the cost of decreasing precision. In order to find an appropriate trade-off, two basis functions named Laguerre functions and Haar functions, are tested in this paper. MPC with Laguerre functions decreases more computational load while MPC with Haar functions offers a more accurate solution. The approach is not restricted to Laguerre functions or Haar functions, users can select their own basis functions for different applications and preferences.

Real-time walking pattern generation for a lower limb exoskeleton, implemented on the Exoped robot

Lower extremity exoskeletons have been developed as a motion assistive technology in recent years. Walking pattern generation is a fundamental topic in the design of these robots. The usual approach with most exoskeletons is to use a pre-recorded pattern as a look-up table. There are some deficiencies with this method, including data storage limitation and poor regulation relating to the walking parameters. In addition, the walking parameters can be taken in hand very hard. Therefore modeling the human walking pattern is required. The few existing models provide piece by piece walking patterns, only generating at the beginning of each stride. In this paper, a real-time walking pattern generation method is provided which enables changing the parameters during the stride. For this purpose, two feedback controlled third order systems are proposed as real-time trajectory planners for generating the trajectories of the x and y components of each joint’s position. The boundary conditions of the trajectories are determined to prevent backward balance loss by appropriate displacement of the center of mass. In addition, a cost function is intended for each trajectory planner in order to increase the smoothness of trajectories. Optimization technique is used to design the feedback controller for tracking the boundary conditions in such a way that the cost function is minimized. Finally, the proper joint angles are generated using inverse kinematics transformation. The performance of the proposed pattern generator is verified via real experiments on the Exoped robot.

Real-time continuous ZMP pattern generation of a humanoid robot using an analytic method based on capture point

ABSTRACTThis paper introduces an analytic method to generate a continuous ZMP pattern based on a capture point (CP). When a target CP is decided in real-time, the pattern generator makes the CP, ZMP, which it is within convex hull of the supporting feet area, and CoM patterns without discontinuity by closed-form solutions for a single step. Therefore, the proposed pattern generation method does not need a ZMP pattern modification, numerical iterations, and future ZMPs. The method is employed to treat applications such as step length change while walking and push recovery during walking in place. Furthermore, since compliant characteristics such as body oscillation appear in the humanoid robot, we introduce a system model, a double inverted pendulum model with flexible joints for the model-based control. Finally, the real-time walking pattern generation method and the walking control scheme are verified by experiments with the humanoid robot HUBO2.

Real-time Walking Pattern Generation for a Biped Robot with Hybrid CPG-ZMP Algorithm

Biped robots have better mobility than conventional wheeled robots. The bio-inspired method based on a central pattern generator (CPG) can be used to control biped robot walking in a manner like human beings. However, to achieve stable locomotion, it is difficult to modulate the parameters for the neural networks to coordinate every degree of freedom of the walking robot. The zero moment point (ZMP) method is very popular for the stability control of biped robot walking. However, the reference trajectories have low energy efficiency, lack naturalness and need significant offline calculation. This paper presents a new method for biped real-time walking generation using a hybrid CPG-ZMP control algorithm. The method can realize a stable walking pattern by combining the ZMP criterion with rhythmic motion control. The CPG component is designed to generate the desired motion for each robot joint, which is modulated by phase resetting according to foot contact information. By introducing the ZMP location, the activity of the CPG output signal is adjusted to coordinate the limbs’ motion and allow the robot to maintain balance during the process of locomotion. The numerical simulation results show that, compared with the CPG method, the new hybrid CPG-ZMP algorithm can enhance the robustness of the CPG parameters and improve the stability of the robot. In addition, the proposed algorithm is more energy efficient than the ZMP method. The results also demonstrate that the control system can generate an adaptive walking pattern through interactions between the robot, the CPG and the environment.

Real-Time Walking Pattern Generation Method for Humanoid Robots by Combining Feedback and Feedforward Controller

This paper focuses on real-time walking pattern generation for humanoid robots with linear inverted pendulum model (LIPM). In general, there are many issues in generating proper walking patterns of center of mass and zero moment point (ZMP) with the LIPM since the LIPM has two drawbacks such as instability and non-minimum phase property. For resolving these difficulties, the paper proposes a new real-time approach by combining a feedback and a feedforward controller. The feedback controller employs a pole placement method which shifts the poles of the LIPM in order to improve system stability. The feedforward controller utilizes advanced pole-zero cancelation by series approximation method (APZCSA) for reducing non-minimum phase property which occurs by an unstable zero and is not able to be dealt with by the feedback controller. In addition, the APZCSA improves the tracking error induced by finite series approximation. Using the two controllers, the proposed method makes the transfer function of overall walking pattern generation system approximately unity and consequently generates a stable walking pattern which follows a desired ZMP according to walking path. The efficiency of the proposed method is verified by walking pattern planning examples and experiments with the humanoid robot MAHRU-R.

ヒューマノイドロボットの全身動作と足の着地位置の同時計画(機械力学,計測,自動制御)

This paper proposes a method for simultaneously planning the whole-body-motion and the foot-place for a humanoid robot dynamically walking on the flat ground. As constraint conditions imposed on the planner, we consider the differential equation of the robot's motion. To solve this constraint, we use the real-time walking pattern generator. We randomly sample the configuration space to search for the path connecting the start and the goal configurations. When sampling the configuration space, a few milestones are sequentially connected to the parent milestone. To show the effectiveness of the proposed method, we show an experimental result where the humanoid robot HRP-2 avoids the obstacle dynamically walking on the ground.