Unified control of n-link underactuated manipulator with single passive joint: A reduced order approach

Robust balancing control of flexible inverted-pendulum systems

“…In the particular case where = 0 (matched disturbance only), * = 0 is a stable equilibrium for the closed-loop (3)- (10). Differently from Hinfinity and optimal control approaches [14,17], control (10) does not require linearization of the system dynamics around the equilibrium and does not assume prior knowledge of the disturbance bounds.…”

“…Finally, control (10) can balance the inverted-pendulum starting from an initial position ∈ (− /2; /2) arbitrarily far from the equilibrium. This is achieved without linearizing the equations of motion and does not assume prior knowledge of the disturbance bounds, which is in contrast with optimal and H-infinity control [14,17]. To highlight this point a further simulation was conducted with initial position = 0; = 0.90 ( Figure 6).…”

“…In summary, flexible mechanisms are typically underactuated since they possess more DOF than actuators. Within this category, inverted-pendulum systems are particularly valuable from a theoretical standpoint and have been serving as models for wheeled robots [13], robotic fingers and manipulators [14], and foldable structures [15]. Additionally, the flexible inverted-pendulum represents an interesting starting point for the study of robot-assisted needle insertion in percutaneous interventions [16], which motivates this work.…”

“…The balancing control of inverted-pendulum systems typically aims to stabilise the upright position, which is unstable in open-loop. In this respect, optimal control [14], H-infinity control [17], and energy-shaping [18] are among the most notable approaches. In particular, energy-shaping control aims to appropriately define the total energy of the closed-loop system enforcing a strict minimum at the desired equilibrium and relies on either Euler-Lagrange or Hamiltonian formulation.…”

Energy-based design of elastic joints for inverted pendulum systems with input saturation

“…Inverted pendulum systems represent an important class of underactuated mechanisms and have been attracting increasing interest in the control and robotics community serving as models for wheeled robots [1], robotic fingers [2], manipulators [3], walking robots [4], and foldable structures [5]. Balancing control of inverted pendulum systems aims to stabilize the upright equilibrium employing a variety of approaches including optimal control [3], H-infinity control [6], and energy-shaping [7]. In particular, energy-shaping control enforces a minimum of the closed-loop potential energy at the desired equilibrium, and is applicable to a wide range of underactuated mechanisms [8].…”