## 1 Introduction  
When the motion-related region of the brain is damaged by a stroke, the body cannot execute its desired movements. In many stroke-paralyzed patients, the neural network controlling the paralyzed limb shrinks because the limb is not used, causing further functional depression. This scenario constitutes a vicious circle [1, 2]. Current rehabilitation methods passively repeat simple repetitive movements, which are unlikely to reconstruct the neural network of the damaged brain. Some studies have reported that voluntary movements and their expression in the brain are important for the recovery of motor function [3, 4]. The sense of motion is usually perceived during a motion, but can be generated in the absence of motion. A visually induced kinesthetic illusion instills the sense of body movement when the body is moving neither voluntarily nor passively. Such an illusion increases the excitability of corticospinal tracts during voluntary movement and activity in the premotor and supplementary motor areas of the brain [5]. The stimulus immediately increases the quantity of electromyograms and improves the motion range of the joint [6]. As a stroke patient cannot easily recall the correct image for relearning a motion, some therapists generate an illusionary image using a mirror and a head mount display. Mirror therapy presents the movement of the unaffected limb in a mirror, creating the impression that the limb on the affected side is moving. Illusion-based rehabilitation is applied to dynamic motions such as walking [7]. This paper presents an illusionary system that induces the sense of stair-climbing without walking on physical stairs. In the present VR technology, the immersive feeling to the virtual environment can be improved by using a head-mounted display (HMD). The following literature is cited as research on VR. There are kinesthetic presentation systems by VR [8], kinesthetic presentation systems by VR with a tactile interface [9], and kinesthetic presentation systems by visual and force sense [10]. The visual information from images alone is not immersive enough, we incorporate walking movements into the virtual environment. Space-perception operations in a virtual reality environment allow redirected walking [11] and an infinite walking locomotion interface [12] even in a narrow space. Users walking in real space can recognize the ground and space situation in both virtual reality and real space environments. This cross-modal phenomenon improves the illusion intensity. When the brain interacts with stimuli received from multiple sensory organs, it complements missing senses and generates a different sense of motion. [PERSON] et al. induced the weight sensation of a virtual object colliding with a hand by stimulating the skeletal hand muscles with electrical signals and vibrations [13]. [PERSON] et al. proposed a cross-modal system that imparts the sensation of ascending and descending stairs [14]. In this conventional system, a sense of stair-climbing is passively achieved when the user steps on physical protrusions. This system exploits the tendency of humans to unconsciously step on the edges of stairs, recalling the sense of stair-climbing [15]. However, the protrusions in this stair-climbing system must be installed in the appropriate position, and are spatially restricted. A system that induces a sense of stair-climbing in a wearable configuration is expected to be more widely applicable. Our system generates an illusion of stair-climbing by reproducing the muscle sense corresponding to the stair-climbing motion in the virtual environment. The user receives a visual presentation and wears a force-feedback device (see Figure 1). The force feedback is provided by actuators that behave as artificial muscles. The generation of muscle activity by force feedback, which provides the illusion of stair-climbing while walking on a flat level, is the main contribution of this paper.