Bram Demeulenaere

Time-Optimal Path Tracking for Robots: A Convex Optimization Approach

This paper focuses on time-optimal path tracking, a subproblem in time-optimal motion planning of robot systems. Through a nonlinear change of variables, the time-optimal path tracking problem is transformed here into a convex optimal control problem with a single state. Various convexity-preserving extension are introduced, resulting in a versatile approach for optimal path tracking. A direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method.

Extended LMI characterizations for stability and performance of linear systems

Over the past ten years, extensive research has been devoted to extended LMI characterizations for stability and performance of linear systems. These characterizations constitute a valuable tool for reducing conservatism in hard problems like multi-objective control, and robust stability and performance analysis. The present paper proposes a general, projection lemma based methodology for deriving such extended LMIs and hereby provides a straightforward and unified proof for all known literature results as well as some currently missing extended LMIs.

Brief paper: Robust high-order repetitive control: Optimal performance trade-offs

High-order repetitive control has previously been introduced to either improve the robustness for period-time uncertainty or reduce the sensitivity for non-periodic inputs of standard repetitive control schemes. This paper presents a systematic, semidefinite programming based approach to compute high-order repetitive controllers that yield an optimal trade-off between these two performance criteria. The methodology is numerically illustrated through trade-off curves for various controller orders and levels of period-time uncertainty. Moreover, existing high-order repetitive control approaches are shown to correspond to specific points on these curves.

Subject-specific hip geometry affects predicted hip joint contact forces during gait

Hip loading affects bone remodeling and implant fixation. In this study, we have analyzed the effect of subject-specific modeling of hip geometry on muscle activation patterns and hip contact forces during gait, using musculoskeletal modeling, inverse dynamic analysis and static optimization. We first used sensitivity analysis to analyze the effect of isolated changes in femoral neck-length (NL) and neck-shaft angle (NSA) on calculated muscle activations and hip contact force during the stance phase of gait. A deformable generic musculoskeletal model was adjusted incrementally to adopt a physiological range of NL and NSA. In a second similar analysis, we adjusted hip geometry to the measurements from digitized radiographs of 20 subjects with primary hip osteoarthrosis. Finally, we studied the effect of hip abductor weakness on muscle activation patterns and hip contact force. This analysis showed that differences in NL (41-74 mm) and NSA (113-140 degrees ) affect the muscle activation of the hip abductors during stance phase and hence hip contact force by up to three times body weight. In conclusion, the results from both the sensitivity and subject-specific analysis showed that at the moment of peak contact force, altered NSA has only a minor effect on the loading configuration of the hip. Increased NL, however, results in an increase of the three hip contact-force components and a reduced vertical loading. The results of these analyses are essential to understand modified hip joint loading, and for planning hip surgery for patients with osteoarthrosis.

Time-energy optimal path tracking for robots: a numerically efficient optimization approach

This paper focuses on time-optimal and time-energy optimal path tracking, which are subproblems in optimal motion planning of robot systems. Through a nonlinear change of variables, the time-energy optimal path tracking problem is transformed here into a convex optimal control problem with a single state variable. A direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Application to a 6-DOF KUKA 361 industrial robot carrying out a writing task illustrates the practicality of the new method.

A physiology based inverse dynamic analysis of human gait: potential and perspectives

One approach to compute the musculotendon forces that underlie human motion is to combine an inverse dynamic analysis with a static optimisation procedure. Although computationally efficient, this classical inverse approach fails to incorporate constraints imposed by muscle physiology. The present paper reports on a physiological inverse approach (PIA) that combines an inverse dynamic analysis with a dynamic optimisation procedure. This allows the incorporation of a full description of muscle activation and contraction dynamics, without loss of computational efficiency. A comparison of muscle excitations and MT-forces predicted by the classical and the PIA is presented for normal and pathological gait. Inclusion of muscle physiology primarily affects the rate of active muscle force build-up and decay and allows the estimation of passive muscle force. Consequently, it influences the onset and cessation of the predicted muscle excitations as well as the level of co-contraction.

Ultimate limits for counterweight balancing of crank-rocker four-bar linkages

This paper focuses on reducing the dynamic reactions (shaking force, shaking moment, and driving torque) of planar crank-rocker four-bars through counterweight addition. Determining the counterweight mass parameters constitutes a nonlinear optimization problem, which suffers from local optima. This paper, however, proves that it can be reformulated as a convex program, that is, a nonlinear optimization problem of which any local optimum is also globally optimal. Because of this unique property, it is possible to investigate (and by virtue of the guaranteed global optimum, in fact prove) the ultimate limits of counterweight balancing. In a first example a design procedure is presented that is based on graphically representing the ultimate limits in design charts. A second example illustrates the versatility and power of the convex optimization framework by reformulating an earlier counterweight balancing method as a convex program and providing improved numerical results for it.

Input torque balancing using an inverted cam mechanism

Input torque balancing through addition of an auxiliary, input torque balancing mechanism, is a well-known way for reducing drive speed fluctuations in high-speed cam-follower mechanisms. This paper develops a methodology to design and optimize the so-called inverted cam mechanism (ICM), a simple, cam-based input torque balancing mechanism. It was already introduced in the 1950s, but the design methodologies proposed by Meyer zur Capellen (1964) and Michelin (1979) are, respectively, erroneous or too rough an approximation, and are corrected here. The describing equation that governs the ICM cam design, is shown to be a second-order, nonlinear, ordinary differential equation. It is solved by parameterizing its solution as a finite Fourier series, the coefficients of which are determined through a nonlinear least-squares problem. Based on this methodology, an ICM is designed for input torque balancing a high-speed, industrial cam-follower mechanism. The ICMs design parameters result from a design optimization, which aims at obtaining a compact and technologically feasible mechanism. The optimization problem is solved using a design chart, which is efficiently created based on a mondimensionalized analysis.

Optimal Performance Tradeoffs in Repetitive Control: Experimental Validation on an Active Air Bearing Setup

In repetitive control, the bode sensitivity integral dictates a tradeoff between improved suppression of periodic disturbances and degraded performance for non-periodic inputs. This paper experimentally demonstrates the implications of this tradeoff by applying a recently developed repetitive controller design approach to reduce the error motion of the spindles axis of rotation on an active air bearing setup. This design methodology translates the performance tradeoff into tradeoff curves between a non-periodic and periodic performance index, of which the practical relevance is illustrated by the obtained experimental results. Second, the relation is investigated between these two performance indices and the adaptive performance of the repetitive controller during large variations of the spindles rotational speed setpoint. The experiments suggest that, although defined for steady state, the two performance indices also relate to the adaptive performance of the repetitive controller.

A physiology-based inverse dynamic analysis of human gait using sequential convex programming: a comparative study

This paper presents an enhanced version of the previously proposed physiological inverse approach (PIA) to calculate musculotendon (MT) forces and evaluates the proposed methodology in a comparative study. PIA combines an inverse dynamic analysis with an optimisation approach that imposes muscle physiology and optimises performance over the entire motion. To solve the resulting large-scale, nonlinear optimisation problem, we neglected muscle fibre contraction speed and an approximate quadratic optimisation problem (PIA-QP) was formulated. Conversely, the enhanced version of PIA proposed in this paper takes into account muscle fibre contraction speed. The optimisation problem is solved using a sequential convex programing procedure (PIA-SCP). The comparative study includes PIA-SCP, PIA-QP and two commonly used approaches from the literature: static optimisation (SO) and computed muscle control (CMC). SO and CMC make simplifying assumptions to limit the computational time. Both methods minimise an instantaneous performance criterion. Furthermore, SO does not impose muscle physiology. All methods are applied to a gait cycle of six control subjects. The relative root mean square error averaged over all subjects, , between the joint torques simulated from the optimised activations and the joint torques obtained from the inverse dynamic analysis was about twice as large for SO ( = 86) as compared with CMC ( = 39) and PIA-SCP ( = 50). was at least twice as large for PIA-QP ( = 197) than for all other methods. As compared with CMC, muscle activation patterns predicted by PIA-SCP better agree with experimental electromyography (EMG). This study shows that imposing muscle physiology as well as globally optimising performance is important to accurately calculate MT forces underlying gait.