Energy-oriented Modeling And Control of Robotic Systems

This research focuses on the energy-oriented control of robotic systems using an ultracapacitor as the energy source. The primary objective is to simultaneously achieve the motion task objective and to increase energy efficiency through energy regeneration. To achieve this objective, three aims have been introduced and studied: brushless DC motors (BLDC) control by achieving optimum current in the motor, such that the motion task is achieved, and the energy consumption is minimized. A proof-ofconcept study to design a BLDC motor driver which has superiority compare to an off-the-shelf driver in terms of energy regeneration, and finally, the third aim is to develop a framework to study energy-oriented control in cooperative robots. The first aim is achieved by introducing an analytical solution which finds the optimal currents based on the desired torque generated by a virtual. Furthermore, it is shown that the well-known choice of a zero direct current component in the direct-quadrature frame is sub-optimal relative to our energy optimization objective. The second aim is achieved by introducing a novel BLDC motor driver, composed of three independent regenerative drives. To run the motor, the control law is obtained by specifying an outer-loop torque controller followed by minimization of power consumption via online constrained quadratic optimization. An experiment is conducted to assess the performance of the proposed concept against an off-the-shelf driver. It is shown that, in terms of energy regeneration and consumption, the developed driver has better performance, and a reduction of 15% energy consumption is achieved. v For the third aim, an impedance-based control scheme is introduced for cooperative manipulators grasping a rigid object. The position and orientation of the payload are to be maintained close to a desired trajectory, trading off tracking accuracy by low energy consumption and maintaining stability. To this end, an optimization problem is formulated using energy balance equations. The optimization finds the damping and stiffness gains of the impedance relation such that the energy consumption is minimized. Furthermore, L2 stability techniques are used to allow for time-varying damping and stiffness in the desired impedance. A numerical example is provided to demonstrate the results

Design, Control, and Optimization of Robots with Advanced Energy Regenerative Drive Systems

We investigate the control and optimization of robots with ultracapacitor based regenerative drive systems. A subset of the robot joints are conventional, in the sense that external power is used for actuation. Other joints are energetically self-contained passive systems that use ultracapacitors for energy storage. An electrical interconnection known as the star configuration is considered for the regenerative drives that allows for direct electric energy redistribution among joints, and enables higher energy utilization efficiencies. A semi-active virtual control strategy is used to achieve control objectives. We find closed-form expressions for the optimal robot and actuator parameters (link lengths, gear ratios, etc.) that maximize energy regeneration between any two times, given motion trajectories. In addition, we solve several trajectory optimization problems for maximizing energy regeneration that admit closed-form solutions, given system parameters. Optimal solutions are shown to be global and unique. In addition, closed-form expressions are provided for the maximum attainable energy. This theoretical maximum places limits on the amount of energy that can be recovered. Numerical examples are provided in each case to demonstrate the results. For problems that don\u27t admit analytical solutions, we formulate the general nonlinear optimal control problem, and solve it numerically, based on the direct collocation method. The optimization problem, its numerical solution and an experimental evaluation are demonstrated using a PUMA manipulator with custom regenerative drives. Power flows, stored regenerative energy and efficiency are evaluated. Experimental results show that when following optimal trajectories, a reduction of about 10-22% in energy consumption can be achieved. Furthermore, we present the design, control, and experimental evaluation of an energy regenerative powered transfemoral prosthesis. Our prosthesis prototype is comprised of a passive ankle, and an active regenerative knee joint. A novel varying impedance control approach controls the prosthesis in both the stance and swing phase of the gait cycle, while explicitly considering energy regeneration. Experimental evaluation is done with an amputee test subject walking at different speeds on a treadmill. The results validate the effectiveness of the control method. In addition, net energy regeneration is achieved while walking with near-natural gait across all speeds

Regenerative Suspension System Modeling and Control

Many energy indicators show an increase in the world’s energy deficit. Demand for portable energy sources is growing and has increased the market for energy harvesters and regenerative systems. This work investigated the implementation of a regenerative suspension in a two-degree-of freedom (2-DOF) quarter-car suspension system. First, an active controller was designed and implemented. It showed 69% improvement in rider comfort and consumed 8 – 9 W of power to run the linear motor used in the experiment. A regenerative suspension system was then designed to save the energy normally spent in active suspensions, approximately several kilowatts in an actual car. Regenerative suspension is preferable because it can regenerate energy. Experimental investigations were then conducted to find generator constants and damping coefficients. Additionally, generator damping effects and power regeneration in the quarter-car test bed were also investigated. The experiments showed that a linear regenerative damper can suppress up to 22% of vibrations and harvest 2% of the disturbance power. Since both harvesting and damping capabilities were noticeable in this test bed, it was used to implement regenerative suspension, and a regenerative controller was developed to provide riders with additional comfort. To implement this regenerative controller, an electronic interface was designed to facilitate controlling the regenerative force and storing energy after the rectification process. The electronic interface used was a symmetrical-bridgeless boost converter (SBBC) due to its few components and even fewer control efforts. The converter was then modeled in a manner that made the current and voltage in phase for the maximum power factor. The converter control allowed the motor’s external load to be presented as of variable resistance with the unity power factor. The generator was then considered a voltage source for energy regeneration purposes. The controller was designed to control regenerative force at a frequency of 20 kHz. This frequency was sufficient to enable another controller to manipulate the desired regenerative damping force, which was chosen to be 1 kHz. The input to this controller was the generator voltage used to determine the polarity of pulse-width modulation (PWM). Therefore, a combination of converter and controller was able to take the place of an active controller. A different controller was then designed to manipulate the desired damping force. This regenerative controller was designed in a manner similar to that of a semi-active controller. It improved vibration suppression and enhanced harvesting capabilities. The regenerative suspension showed better results than a passive suspension. The improvements are minimal at this time, but there is the potential for greater improvement with a more efficient controller. The harvested energy was so small in this experiment because the damper was inefficient. In practice, the damper’s efficiency should be improved. A regenerative damper will be more economical than a passive damper, and suppress more vibration at the same time. The active suspension system showed superior performance. Conversely, the regenerative system showed only modest performance but also regenerated energy. However, a regenerative suspension can be combined with an active suspension to enhance the rider’s comfort and provide energy regeneration

Regenerative Suspension System Modeling and Control

Many energy indicators show an increase in the world’s energy deficit. Demand for portable energy sources is growing and has increased the market for energy harvesters and regenerative systems. This work investigated the implementation of a regenerative suspension in a two-degree-of freedom (2-DOF) quarter-car suspension system. First, an active controller was designed and implemented. It showed 69% improvement in rider comfort and consumed 8 – 9 W of power to run the linear motor used in the experiment. A regenerative suspension system was then designed to save the energy normally spent in active suspensions, approximately several kilowatts in an actual car. Regenerative suspension is preferable because it can regenerate energy. Experimental investigations were then conducted to find generator constants and damping coefficients. Additionally, generator damping effects and power regeneration in the quarter-car test bed were also investigated. The experiments showed that a linear regenerative damper can suppress up to 22% of vibrations and harvest 2% of the disturbance power. Since both harvesting and damping capabilities were noticeable in this test bed, it was used to implement regenerative suspension, and a regenerative controller was developed to provide riders with additional comfort. To implement this regenerative controller, an electronic interface was designed to facilitate controlling the regenerative force and storing energy after the rectification process. The electronic interface used was a symmetrical-bridgeless boost converter (SBBC) due to its few components and even fewer control efforts. The converter was then modeled in a manner that made the current and voltage in phase for the maximum power factor. The converter control allowed the motor’s external load to be presented as of variable resistance with the unity power factor. The generator was then considered a voltage source for energy regeneration purposes. The controller was designed to control regenerative force at a frequency of 20 kHz. This frequency was sufficient to enable another controller to manipulate the desired regenerative damping force, which was chosen to be 1 kHz. The input to this controller was the generator voltage used to determine the polarity of pulse-width modulation (PWM). Therefore, a combination of converter and controller was able to take the place of an active controller. A different controller was then designed to manipulate the desired damping force. This regenerative controller was designed in a manner similar to that of a semi-active controller. It improved vibration suppression and enhanced harvesting capabilities. The regenerative suspension showed better results than a passive suspension. The improvements are minimal at this time, but there is the potential for greater improvement with a more efficient controller. The harvested energy was so small in this experiment because the damper was inefficient. In practice, the damper’s efficiency should be improved. A regenerative damper will be more economical than a passive damper, and suppress more vibration at the same time. The active suspension system showed superior performance. Conversely, the regenerative system showed only modest performance but also regenerated energy. However, a regenerative suspension can be combined with an active suspension to enhance the rider’s comfort and provide energy regeneration

Hybrid Electromagnetic Vibration Isolation Systems

Traditionally, dynamic systems are equipped with passive technologies like viscous shock absorbers and rubber vibration isolators to attenuate disturbances. Passive elements are cost effective, simple to manufacture, and have a long life span. However, the dynamic characteristics of passive devices are fixed and tuned for a set of inputs or system conditions. Thus in many applications when variation of input or system conditions is present, sub-optimal performance is realized. The other fundamental flaw associated with passive devices is that they expel the undesired kinetic energy as heat. Recently, the introduction of electromagnetic technologies to the vibration isolation systems has provided researchers with new opportunities for realizing active/semi-active vibration isolation systems with the additional benefit of energy regeneration (in semi-active mode). Electromagnetic vibration isolators are often suffer from a couple of shortcomings that precludes their implementations in many applications. Examples of these short comings include bulky designs, low force density, high energy consumption (in active mode), and fail-safe operation problem. This PhD research aims at developing optimal hybrid-electromagnetic vibration isolation systems to provide active/semi-active and regenerative vibration isolation for various applications. The idea is to overcome the aforementioned shortcomings by integrating electromagnetic actuators, conventional damping technologies, and stiffness elements into single hybrid packages. In this research, for both semi-active and active cases, hybrid electromagnetic solutions are proposed. In the first step of this study, the concept of semi-active hybrid damper is proposed and experimentally tested that is composed of a passive hydraulic and a semi-active electromagnetic components. The hydraulic medium provides a bias and fail-safe damping force while the electromagnetic component adds adaptability and energy regeneration to the hybrid design. Based on the modeling and optimization studies, presented in this work, an extended analysis of the electromagnetic damping component of the hybrid damper is presented which can serve as potent tool for the designers who seek maximizing the adaptability (and regeneration capacity) of the hybrid damper. The experimental results (from the optimized design) show that the damper is able to produce damping coefficients of 1300 and 0-238 Ns/m through the viscous and electromagnetic components, respectively. In particular, the concept of hybrid damping for the application of vehicle suspension system is studied. It is shown that the whole suspension system can be adjusted such that the implementation of the hybrid damper, not only would not add any adverse effects to the main functionally of the suspension, but it would also provide a better dynamics, and enhance the vehicle fuel consumption (by regenerating a portion of wasted vibration energy). In the second step, the hybrid damper concept is extended to an active hybrid electromagnetic vibration isolation systems. To achieve this target, a passive pneumatic spring is fused together with an active electromagnetic actuator in a single hybrid package. The active electromagnetic component maintains a base line stiffness and support for the system, and also provides active vibration for a wide frequency range. The passive pneumatic spring makes the system fail-safe, increases the stiffness and support of the system for larger masses and dead loads, and further guarantees a very low transmissibility at high frequencies. The FEM and experimental results confirmed the high force density of the proposed electromagnetic component, comparing to a voice coil of similar size. In the proposed design, with a diameter of ~125 mm and a height of ~60 mm, a force variation of ~318 N is obtained for the currents of I=±2 A. Furthermore, it is demonstrated that the proposed actuator has a small time constant (ratio of inductance to resistance for the coils) of less than 5.2 ms, with negligible eddy current effect, making the vibration isolator suitable for wide bandwidth applications. According to the results, the active controllers are able to enhance the performance of the passive elements by up to 80% and 95% in terms of acceleration and force transmissibilities, respectively

Optimal Mixed Tracking/Impedance Control With Application to Transfemoral Prostheses With Energy Regeneration

We design an optimal passivitybased tracking/impedance control system for a robotic manipulator with energy regenerative electronics, where the manipulator has both actively and semi-actively controlled joints. The semi-active joints are driven by a regenerative actuator that includes an energy-storing element. Method: External forces can have a large influence on energy regeneration characteristics. Impedance control is used to impose a desired relationship between external forces and deviation from reference trajectories. Multi-objective optimization (MOO) is used to obtain optimal impedance parameters and control gains to compromise between the two conflicting objectives of trajectory tracking and energy regeneration. We solve the MOO problem under two different scenarios: 1) constant impedance; and 2) timevarying impedance. Results: The methods are applied to a transfemoral prosthesis simulation with a semi-active knee joint. Normalized hypervolume and relative coverage are used to compare Pareto fronts, and these two metrics show that time-varying impedance provides better performance than constant impedance. The solution with time-varying impedance with minimum tracking error (0.0008 rad) fails to regenerate energy (loses 9.53 J), while a solution with degradation in tracking (0.0452 rad) regenerates energy (gains 270.3 J). A tradeoff solution results in fair tracking (0.0178 rad) and fair energy regeneration (131.2 J). Conclusion: Our experimental results support the possibility of net energy regeneration at the semi-active knee joint with human-like tracking performance. Significance: The results indicate that advanced control and optimization of ultracapacitor-based systems can significantly reduce power requirements in transfemoral prostheses

An analytical and numerical study of magnetic spring suspension and energy recovery mechanism

As the automotive paradigm shifts towards electric, limited range remains a key challenge. Increasing the battery size adds weight, which yields diminishing returns in range per kilowatt-hour. Therefore, energy recovery systems, such as regenerative braking and photovoltaic cells, are desirable to recharge the onboard batteries in between hub charge cycles. While some reports of regenerative suspension do exist, they all harvest energy in a parasitic manner, and the predicted power output is extremely low, since the majority of the energy is still dissipated to the environment by the suspension. This paper proposes a fundamental suspension redesign using a magnetically-levitated spring mechanism and aims to increase the recoverable energy significantly by directly coupling an electromagnetic transducer as the main damper. Furthermore, the highly nonlinear magnetic restoring force can also potentially enhance rider comfort. Analytical and numerical models have been constructed. Road roughness data from an Australian road were used to numerically simulate a representative environment response. Simulation suggests that 10’s of kW to >100 kW can theoretically be generated by a medium-sized car travelling on a typical paved road (about 2–3 orders of magnitude higher than literature reports on parasitic regenerative suspension schemes), while still maintaining well below the discomfort threshold for passengers (<0.315 m/s 2 on average)