## 1 Introduction  
The main problem faced by disabled people using wheelchairs are terrain obstacles, either architectural or natural ones, such as thresholds, hills, or surface irregularities. All these factors translate into increased resistance during wheelchair propulsion. To facilitate wheelchair propulsion for people with disabilities, scientists and inventors are developing innovative design solutions for suspension systems, propulsion systems, etc. An innovation in the field of wheelchair propulsion systems are wheelchairs with electric-manual hybrid propulsion systems that allow people with disabilities to manually propel the wheelchair and use the support of the drive torque generated by electric motors. From the experience of users of such wheelchairs, most of them consider this solution to increase their mobility and social integration [1]. It allows them to increase their traveling distance [2], and facilitates tasks requiring increased torque on the propulsion wheels [3]. Despite their advantages, hybrid propulsion systems also have drawbacks, such as: difficulty to transport in a vehicle [1,3], limited battery life [1], limited use inside the home [3], the need to take into account control delay characterized by unnatural interaction with the user [3, 4, 5]. What is particularly noticeable is reduced precision of control compared to classic wheelchairs [3], due to the increased weight, size and the possibility of delay of control signals [6]. In addition, there is a risk that users of wheelchairs with assisted-propulsion systems might lead a less active lifestyle limiting their physical development, which may, in turn, predispose them to many long-term health problems [6]. An important aspect when designing and using wheelchairs with propulsion assistance systems is the use of control algorithms. Literature on the subject presents practical and effective algorithms for interference suppression to ensure safe and comfortable operation [7]. These algorithms can detect and suppress external forces not related to the propulsion by human hands [7]. [PERSON] and [PERSON] (2013) describe algorithms that respond to gravitational forces acting on slopes [7]. Research is also being carried out on optimal cross-coupling control strategies, which were applied to a rim motor wheelchair, with the aim of adjusting the speed ratio of the left and right wheels in order to follow specified paths with various turning radius [8]. In general, one can distinguish the concept of assisted-propulsion control, which assumes increasing the torque applied to the wheels by the user [9]. [PERSON] et al. [6] with his team point out that propulsion assistance technology supports mobility and plays an important role in the design of wheelchairs in terms of: wheelchair mechanics, the mobility of the user, and the interface of the wheelchair user. The design used in the research according to the patent application P.427855 [10] described in the book \"Research on the biomechanics of manual wheelchair drive for innovative manual and hybrid drive\" [11] equipped with additional propulsion systems, is consistent with modern wheelchair design trends. The modular structure of the developed propulsion system makes it possible to adapt it to most mass-produced wheelchairs. Available propulsion modes such as: purely manual or electric propulsion systems and hybrid modes, i.e., hill-climbing assistance and assistance with torque in the propulsive phase make the described design innovative and consistent with contemporary design trends. The functions of the wheelchair hybrid propulsion system are consistent with the description of trends in wheelchair development technology indicated by [PERSON] and his team [12]. These trends relate to the increased safety of use, efficiency, accessibility and, above all, increased mobility of disabled people [12].