When using crutches or sticks to support movement, you move the sticks forwards, then lean on them to pivot the body forward. If the crutch or support were freely hanging from the waist or shoulder of the person, any tilting of the body backward or forward would have the effect of moving the crutch or support forward or backward like a pendulum. When the crutch or support hits the ground, the tilting motion is arrested.
What an inspiring discussion. Some thoughts this discussion provoked 1. The shape, styling and materials of shoes contribute to the problem of instability and tripping. Try to visualise a moderately high arched stylish shoe that is poised upon a base that is stable in two dimensions made from an impact absorbing material that softens on impact preventing tripping. 2 Having lost balance, how to prevent a fall. The pendulum idea working automatically to activate a rigid support in the same way that a person would use a cane 3. Having fallen, how to get up, imagine a collapsible telescopic cane that with pneumatics or hydraulics can be used to lift the faller