# Research on Optimal Control of Treadmill Shock Absorption Based on Ground Reaction Force Constraint
## 1 Introduction  
Running is one of the best ways to reduce the various harms associated with prolonged sitting, eliminate negative physiological states, and alleviate psychological stress. It is the most popular form of physical exercise in China and has the highest participation rate. With the development of the times, more and more people are choosing to exercise indoors on treadmills. During running, the vertical ground reaction force can be 2 to 5 times the body weight [1]. Correspondingly, the increasing popularity of running has led to a higher incidence of running-related injuries. Epidemiological studies have found that the knee joint is the most vulnerable part of the body to injury during running [2, 3]. During running, the large and repetitive ground reaction forces (GRFs) on the knee joint can increase the risk of overse injuries [4]. [PERSON] [5] pointed out that during the support phase of jogging, energy is primarily absorbed by the knee joint and generated at the ankle joint. Therefore, having a superior shock absorption system in treadmills is crucial to prevent injuries to the ankle and knee joints of runners. Research indicates that treadmills have the highest shock absorption capability among all surfaces, such as artificial turf and athletic tracks. Treadmills with more shock-absorbing and compliant surfaces are expected to enhance energy return for athletes [6]. Shock-absorbing treadmills generally reduce foot pressure and stress during running, with the most significant reductions observed in the forefoot and midfoot areas. Impact forces typically increase with speed [7]. There are subtle differences in the electromyography (EMG) signals of leg muscles between running on the ground and running on a treadmill [8]. [PERSON] set multiple springs between the two sides of the running belt plate and the bottom frame to realize the spring shock absorption of the treadmill [9]. [PERSON], [PERSON] set elastic pads between the treadmill frame and the body of the support wheel to realize shock absorption of the treadmill rubber pad [10]. [PERSON], [PERSON] installed two magnetically repelling magnets on the lower side of the support plate and the upper side of the frame of the treadmill base to achieve magnetic suspension shock absorption of the treadmill [11]. [PERSON] implemented shock absorption through multiple air suspension elements [12]. The shock absorption systems mentioned above are primarily passive, relying on nonadjustable methods or manual changes to rubber pads. Adjusting the hardness of the rubber or changing the number of springs is often aimed at simulating different running surfaces, such as grass or synthetic tracks. However, these systems cannot actively adjust treadmill shock absorption based on the magnitude of ground reaction forces (GRFs). This makes operation cumbersome and limits precise regulation, reducing their effectiveness in preventing exercise-related injuries. The peak foot pressure is the most direct indicator of the magnitude of ground reaction force (GRF). GRF represents the reaction force exerted by the ground on the foot during running when it makes contact with the surface. In light of current research, this paper proposes a control system for treadmills that actively adjusts the shock absorption based on the magnitude of GRF. This paper establishes an active control system for treadmill shock absorption through system modeling and experimental setup. The designed treadmill is modified from a standard rubber-bottom treadmill. The hardware components include airbags, air tubes, a pump, solenoid valves, relays, a pressure sensor, a microcontroller, a safety valve, a host computer, and foot pressure sensors. This treadmill can actively adjust its shock absorption based on the specified dataset. The actively controlled shock absorption treadmill offers a multilevel adjustment feature compared to conventional shock-absorbing treadmills. It can more effectively and accurately reduce peak foot pressure during running, resulting in improved shock absorption.