# Adaptive Prosthetic Trajectory Estimation Based on Key Points Constraints
###### Abstract  
Lower limb knee-ankle prostheses can effectively assist above-knee amputees in completing their basic daily activities. This study explored methods for estimating the joint kinematics of intelligent lower limb prostheses to better adapt them to the walking requirements of amputees. A method of estimating the knee and ankle joint trajectories under different speeds and slopes was raised. The joints of a prosthetic need to have a movement trajectory similar to that of the joints of healthy individuals, taking into account the person's motion intentions and complying with the law of movement. In this study, a prosthetic kinematics estimation method was studied to realize continuous speed and slope adaptation through key points. The iterative Douglas-Peucker algorithm automatically found the key points of the kinematic trajectory curve, and an invariant basis function-fitting model with key points constraints was constructed. Finally, the radial basis function neural network was used to estimate the adaptive task function of the parts affected by the speed and slope, resulting in an overall kinematics estimation model. Our experiments verified the effectiveness of the proposed method, which accurately estimated the kinematic trajectory; the knee and ankle joint estimation errors were greatly reduced compared to those obtained with previous methods, facilitating further research on individual algorithms. intelligent prosthesis control; adaptive kinematic estimation; gait key points Article  
Adaptive Prosthetic Trajectory Estimation Based on Key Points Constraints  
while also avoiding noticeable impacts or vibrations that could make the walking process uncomfortable. To achieve this, a kinematic model is established for both the prosthesis and the human body, allowing for the position and attitude of the prosthesis to be calculated based on the corresponding phase variables. Additionally, the model needs to be able to adapt to changes in walking speed and slopes, dynamically adjusting the motion trajectory of the prosthetic limb according to the real-time speed and slope information collected. Previous studies have shown that different gait speeds and slopes during walking can change the gait trajectory shapes [5; 6; 7]. While gait information can be collected through experimental measurement at various speeds and slopes, this method results in a discontinuous database relative to the task variables and requires a large amount of data to be collected, making it unsuitable for human experiments. Therefore, it is necessary to build a continuous model of gait kinematics to enable adaptive adjustment to the expected kinematic trajectory during walking. Studies in the field of prosthetic control generally adopt three-layer control structures [8], with the upper layer detecting the wearer's intention and determining the walking state. The middle layer generates the desired joint trajectory, and the lower layer controls the actuators to the desired position or torque. In 2016, [PERSON]'s team proposed a gait kinematics modelling method based on the virtual constraint control method. This method considers walking state differences, such as changes in speed and slope [9], and models gait kinematics as a continuous function of gait phase, walking speed, and ground slope. The virtual constraint controller provides the required trajectories over continuous gait stages and movement patterns. In 2017, the team clarified the definition of task function in the optimization algorithm [10], and introduced model order reduction, motion range restriction, and anti-jitter into the algorithm. In 2021, the team further analyzed the potential sources of prediction errors, which were deviations from the average kinematics [11]. The main method of prosthetic control is based on gait phase, including time-based control [12; 13; 14], echo control [15], central pattern generator-based control [16; 17; 18], finite state impedance (FSM) control [19; 20; 21; 22; 23; 24; 25], and more.