Modeling and Control of a Seven Axes Hybrid Electric/Pneumatic Robot Arm

Abstract

Passively compliant drive concepts are often used in bio-inspired robot designs. Especially fluidic artificial muscles share many characteristics with their natural counterparts. Industrial manipulators can benefit from the increased robustness and safety (in contrast to rigid drives) especially in cooperative human/robot environments. We compare different model-based control concepts for a single rotational joint actuated by two fluidic muscles in combination with proportional valves. While the complete valve and muscle models are already included in this setup, the mechanical model becomes more complex when we extend the control to a full seven axes articulated robot arm with both, electrically and pneumatically actuated joints. In this case the Projection Equation in subsystem description is used for the multibody model, allowing a straight-forward realtime application to different robot kinematics. Remaining model errors and disturbances are handled by observer algorithms. We present measurement results and compare them to simulation outputs. Besides the position control, possible approaches for sensorless external force estimation are discussed. They take advantage of the compliance of the robot and are again based on the actuator and multibody models. The considered robot (see Figure 1) is mainly actuated by so-called pneumatic artificial muscles (PAM) [1] -fibre reenforced rubber tubes, which contract when filled with air. The static pulling muscle force F can be modeled by, where p is the internal pressure, h the muscle contraction and a(h) and b(h) are polynomials used to approximate the nonlinear relation between the contraction and the force.A pneumatic rotational joint is actuated by two antagonistically arranged PAMs 1 and 2. The contractions, h 1/2 = h 0 ± r/l (q − q 0 ) 100 %, are both uniquely defined by the joint angle q and construction parameters (acting radius r, muscle length l, angle q 0 , where both muscles have the same contraction h 0 ). The generated torque Q = r (F 1 −F 2 ) is affine in the pressures and can be written as Q = A(q) 0.5 (p 1 + p 2 ) + B(q) (p 1 − p 2 ) + C(q) with some functions A, B and C, which can be calculated from the single muscle characteristics or identified pointwise on the real system. Figure 2 shows the comparison between the measured (thick line) and the nominal muscle model (thin line). A locally (only around Q 1 = 0) calibrated model (light line) has been added for reference. The validation maneuver used in this figure is a slow left/right movement, which means that the actual torque is always close to zero. Beside the differences in the models, a common hysteresis loop is visible in all three curves. This is not yet accounted for in our model and will be subject to further research.The underlying control loop for the muscle pressures is flatness based (see, for example [3]) with the pressure dynamicṡ p V + pV =ṁ R S T . The current muscle volume V depends only on the contraction and can therefore also be calculated from the joint angle. The absolute temper...